Contrary to what you claim, applying the rules is entirely consistent and without problem. We are dealing here with Multiple Combat and Break Tests, the rules of which (as said before) one will find on p.60.
The parent unit is steadfast from the moment it has been defeated but still more ranks after combat resolution than all (any) enemy it is in combat with, and until it has taken its break test.
No. Your argument is inherently contradictory and therefore cannot be the correct interpretation.
You are hanging your hat on the phrase "If a defeated unit has more ranks than its enemy, it takes its Break test on its unmodified leadership. "
(while completely ignoring other phrases such as "a unit that outranks its enemy is considered steadfast")
If that is what steadfast is, then steadfast exists ONLY during the INSTANT you roll for your break test. Because steadfast is the state of being a losing unit with more ranks making a break test and ignoring the combat modifier. It does not come into effect when you lose combat: it only comes into effect during the break test.
Therefore it cannot be passed along to detachments. And if it was passed along to detachments, what would you be passing along? Are you passing along the text "If a defeated unit has more ranks than its enemy, it takes its Break test on its unmodified leadership. " ? Because that does nothing for a detachment. A detachment already has those rules.
Are you passing along the special rule 'Steadfast'? But according to you that doesn't exist.
What text, precisely, do you think is passed along from the parent to the detachment?
And where in the rules, precisely, do you pull support for a unit getting steadfast immediately and only at the conclusion of combat? There are only two possible times you can gain steadfast, depending on interpretation
1) By being engaged with an enemy unit with fewer ranks (always in a building) which happens at the moment combat begins and lasts until you no longer have more ranks or combat ends.
2) At the instant of making a break test if you have more ranks, which ceases at the instant the break test is done. There is no window in between combat ending and break tests starting when steadfast could be applied and passed down, because it exists only when you start the break test, and disappears as soon as the break test is done. According to your interpretation.
You are trying to imagine some 3rd option that appears nowhere, because if we use your interpretation and the rules as written, the whole thing simply doesn't work. At all.
The way it works, in your model is:
Combat
Combat Resolution
Determine Losing Side
Choose order of break tests
Parent Unit
Determine if steadfast
Apply break test. (steadfast goes away at conclusion of break test)
Next unit
Detachment. Parent not steadfast, rule does nothing.
Etc
All this complicated song and dance and having to ignore some rules and invent others in order to bodge together a halfway working scenario is a clue that your interpretation is not accurate.
If we go with what the rulebook actually says "a unit is steadfast if it has more ranks thatn its enemy..." then the whole thing becomes much, much, much simpler and more consistent.
For your interpretation to work, there would have to be a phrase saying 'A defeated unit with more ranks than its opponent gains steadfast immediately after combat resolution, which lasts until the end of the combat phase'. Do we see such a rule? Nope.
For my interpretation to work, we'd need to see a rule saying " If a unit has more ranks than its enemy, then it is steadfast". Do we see such a rule? Why, yes! Yes we do.
In the end, it's very simple:
If steadfast is the state of having more ranks than your enemy, a parent unit that has more ranks than its engaged enemy passes along steadfast to detachments within 3". Neither the parent nor the detachments will need to add negative combat modifiers when making break tests.
If steadfast is the state of a losing unit having more ranks making a break test, a parent unit can never meaningfully pass along steadfast to a detachment in any situation, because steadfast comes into being immediately before the roll and is immediately destroyed after the roll. Once your detachment is making a break test, the parent unit is no longer making a break test and is thus no longer steadfast These are the only two real options afforded by the rules. Separate or same combats don't enter into it and are red herrings.