Combat Detachments seem like a terrible idea, when you can achieve a lot of the same thing by other means (such as screening units to take the charge on their turn, so you can charge in your own, using greatswords with FBIGO, etc.)
The idea of combat detachments (at least in my head) is that they are deployed back from the parent unit to make them difficult to charge. They then become a force multiplier if the parent unit is charged because they can counter charge. It is a more defensive style. In this maybe spearmen would be better than halberdiers for the extra attacks.
I think that the state troops regiments are slightly small. I would cut that second unit of halberdiers into two detachments of 10 each and cut out 2 of the missile detachments to add bulk to the remaining halberdiers.
If I cut the second regiment in half then I loose all four detachments of crossbows and all pretence at shooting.
Wouldn't dropping to one unit of infantry be a nonsense? At that point they're open to being overwhelmed and destroyed in short order.
Maybe but infantry in TOW is hard to destroy when it is large. Big infantry blocks properly supported don't often run and with combat detachments can be expected to win combat reasonably often.
1 infantry block with 2 combat detachments is somewhere between 18 and 24 inches wide depending on how the are deployed. If you deploy 24 infantry in a 7X4 (ish. It'll be three full ranks of 7 with the extra 3 models in the fourth rank) with the combat detachments deployed 7 wide then that formation takes up 21 inches of table space in just models and a further 2-6 inches in distance between the blocks.
You have a lot of Demigriffon knights to protect their flanks as well. I would not be that worried about being overwhelmed. In fact I'd be more concerned that your 20 strong infantry blocks will be overwhelmed.
Plus, the demi contributes First Charge if you can pull it off, making a first turn they charge absolutely devastating!
Does half the unit not need to have first charge to get it?