Simple thing to do (but maybe 'orrible to balance) would be give some general buff to each faction for having X points total in a particular tech tree.
So if you're Umber (and why WOULDN'T you be?) your troops would get +1 attack per 4 techs unlocked in Warfare.
Ha, and maybe lose 0.5 attack per tech unlocked in Civilisation.
That sort of thing - only balanced. Probably easier to balance with quite weak effects, like 2% off unit pay, or 1% off spell costs, or 2% more hitpoints, or whatever, per tech researched (or some other value per point in the tech tree).
Then you might nab a quick tech that you don't need much, just to increase your buff, and if there was a negative effect / debuff tree for your faction, you might have to aim for very specific techs, avoiding stuff you don't absolutely need, and actually trying not to get those points in trade in case you end up with accidental techs.
...so when you're one faction, you'd be looking not only how the tree helps your factional traits, but also how to limit the damage / maximize the advantages of specific trees.
To keep it simple, make sure each faction has only one effect, and then one positive tree, and one negative. Eg:
Umber: +2% hit points per tech in Warfare; -1% hit points per tech in Civilisation.
That sorta thing.