(( The Peacemaker,
Some replies to your questions and thoughts.
1) For your BSB, I'd suggest keeping him on foot, with the main infantry block. A Bare-bones-BSB is fairly cheap, gets a decent Armor Save, and even gets Parry. Having him on foot with the Halberds should keep the 12" LD-re-roll bubble centered fairly well in your army. It also lets him give your Halberds a bit of a boost to melee.
1-A) Plus, you can get your BSB a Pistol too. Each turn you can shoot with the Pistol. Kill one elf, pistol pays for itself.
2) "YMMV" means "Your Mileage May Vary". It means that the item or skill or whatnot has some uses, but it isn't universally/meta useful.
2-A) As such, in my experience, the Earthing Rod isn't worth the cost. Yes, it can let you re-roll a Miscast roll... but that also means that you have to miscast... and then get a miscast result that isn't ignore-able (id est, a result like YOU MAGE DIE). Results like "lose d6 power dice" aren't the end of the turn... or the game. So, to me, those results are ignore-able. Shoot, some of the results give you free hits you on enemy units.
2-A-1) Overall, for a few points over the cost of the Earthing Rod, you can get your wizard a 5+ Ward Save item. That Ward Save is a lot more universal than a re-roll to a miscast roll. Not to mention, that the Wizard can use the Ward Save on a couple of the Miscast events.
2-B) I've seen considerably more 6d6 casts that did not get the Irresistible Force / Miscast result, than those that have gotten the result.
2-C) Empire is magic-weak... but we do have a couple of advantages in magic. The biggest advantage we have is our magicians are fairly cheap, all things considered. The other advantage is that we have access to all the Main Rule Book lores of magic. We're not limited to Beasts and Life for example.
2-C-1) I would suggest that, since you're going to a tournament, stick with magic spheres you're familiar with... or ones that are point-and-click, such as Fire.
2-C-2) I'd also suggest keeping the Level 4 wizard. More spells, and +4 to cast / dispel is a huge advantage.
2-C-3) Also, don't forget, you can thin-cast spells too. "Thin-Cast" is what my group has nicknamed when you cast spells with the bare-minimum d6s required. For example, a Level 2 Fire Wizard can attempt to thin-cast a basic Fireball spell (5+ Target) on 1d6, and still have a 67% chance of casting the spell.
2-C-3-a) For your Level 4 Shadow Mage, you can try to Thin-Cast Super Miasma (d3 lost to MV, WS, BS, and I) on 2d6, and still have about a 50% chance to cast it successfully.
3) The Sword of Striking (+1 to Hit) is good. I just prefer the Sword of Might (+1 to Strength). The Pegasus already puts out a decent amount of Strength 4 attacks, so I figure that the Captain should put out some higher damage attacks.
3-A) I'd keep your White Knight as a lone character, flank charger, war machine hunter. His 10"+3k2" charge move means that he can get flank / rear attacks fairly reliably. While he won't be causing disruption on his own, a Flank Charge does generate +2 CR automatically, and his flank charges can support Demigryph charges.
4) I think you should take a re-look at Swift Reform (pg 95, Main Rule Book). You are missing a huge ability of the musician. Not facing the right way, or about to get flanked? Make the drummer pound out a jaunty tune, pass the LD test, reform facing a new direction, and still be able to take a FULL ACTION.
4-A) Swift Reforms, when passed, let you move your base movement or shoot. That's huge! You can't charge, as charges are declared before movement; but it can keep you from getting flanked by fast movers, or by follow-through attacks.
4-B) Musicians also let you win ties by +1. Doesn't happen much, but it does happen often enough. At least I've seen it happen often enough.
4-C) Musicians give you +1 to LD to Rally. It is a lot easier to rally on a LD 8 over a LD 7. Especially since you're going LD light, with only LD 7 and 8 characters.
4-D) Overall, Musicians aren't the be-all-end-all, but they are highly useful. Their ability to save you precious movement is huge, in a game that rewards mobility and movement.
5) The Champion can accept challenges, keeping your wizard safe for an additional turn.
5-A) Of the three (Standard, Musician, Champ), the Champion is probably the weakest, but he still has his uses.
5-A-1) The upgrade is expensive, for infantry; however, for your Demigryphs, getting the Champ means you now have 1 more STR 6 attack on the charge. Not to mention that the Champion is always removed as the last casualty in the unit (pg 93 - 95, Main Rule Book). Even in the Halberds, you are adding one attack to your front rank. Often times that additional attack helps keep your results in the median bell-curve area.
5-B) Only the base-to-base models can directly target the Champion. Also, only certain abilities (like Sniper) and spells can target individual models. For the most part, the Champ just "hides" with the unit, offering you an extra attack.
5-C) Standard Bearers are fairly standard equipment. They offer the +1 to Static CR... which, often, will just counter the enemy unit Standard Bearer. Still, with Fast Cav usually lacking banners, and enough other unit choices out there who cannot get banners at all, the +1 to static CR does come in handy.
6) Since Archers Skirmish, the ability to Swift Reform (via the Musician) isn't as necessary. However, they still can Panic, and +1 to LD to Rally helps.
6-A) The Champ in your Archer, just gives you one shot that's a bit more accurate. They're still bows... but at least the Champion should be tilting fractional results towards your favor. Id est, 3.5 hits would become 4 hits.
6-B) Over considering it a "Bunker", consider it an "Escort". "Bunker" implies that the Archers are not going to move at all, and just hide all game with the Mage. "Escort" helps remind you that the Archers can still move 8" and fire their bows, all while still protecting the Mage with them, and performing other duties, such as blocking LOS to units behind / beside them.
6-C) Otherwise, if your Mage is just going to hide the whole game, he shouldn't need a bunker at all. He's hidden.
7) Now, as to Banners getting lost in melee. I did say "be Judicious". Demigryphs are pretty buff, but, yes, they can lose fights alone. And there's the key word. Alone. If they are charging a unit by themselves, it is either a target of opportunity or an emergency charge to intercept an enemy charging next turn. When they do this, giving them the +1 to Static CR via the banner will help you keep them in contest to win a fight... or, if they lose, keep them from loosing by an additional CR point.
7-A) Demigryphs should be charging units that are already engaged in melee, or that another unit is charging as well... such as another Demigryph unit or your White Knight. One unit charges the front, while the other unit flank charges. These supported charges increase the number of attacks you're throwing at your opponent, plus potentially have the chance of causing Disruption in your opponents unit (keeping your opponent from getting static CR via Ranks).
8) How are you using your cannons? Are you doing the standard "6 inches in front of that model" sorts of guesses? It sounds like you are getting statistical anomalies resulting in higher-than-expected cannon misfires. A misfire should have a 16% chance... 1-in-6 chance per turn.
8-A) So, with three cannons, you have three, 1-in-6 chances of getting a misfire. Again, that's 3, 1-in-6 chances. It isn't a 3-in-6 chance, as each die and each event is separate. Given that you have three chances, it may seem like you're getting misfires fairly often... when, if you add all the rolls up, you still are getting them at a rate of 16% of the time.
8-B) Anyway, if you're concerned about your misfires coming up more than you feel comfortable with, an Engineer would go a long way to helping mollify that situation... though he'll only help with one cannon or mortar. And, if you get the Volley Gun, he is considerably more of a combat multiplier with the Volley Gun.
8-C) Still, though, three cannons is... to me, points wasted. Cannons have zero multi-purpose ability. You really only get two good turns of shooting, where you can target something you want to shoot at, instead of just stuff hanging around the board. At this point, all your artillery just becomes dead weight.
8-C-1) If you drop a cannon, and grab some Pistoliers, even if the Pistoliers cannot shoot anything, you can always have them hanging out in areas that cause enemy units to not be able to March Move, and to threaten flank / rear charges with the Pistoliers. In other words, the Pistoliers have multiple roles and options open to them during the battle. They can be a lot more dynamic.
Anyway, hope those comments make some sense to you, and give you something to think about. ))