I consider a "perfect" Chapter 3 to be a "clean" Chapter 3, as in, you manage to get all the DF stuff without skipping anything for clean-up reasons, you get all the Ginasta RP except for the Aka maxed one, you ace all the quests (except Trade Negotiations, for that one I think it is silly to care about the best result since it is just confirmed superfluous RP), and you get a smooth 3AW and finish it with 175+ army size.
Of course the question is if it is worthwhile chasing a "perfect" Chapter 3 if it means you having a weaker Chapter 4 and that potentially leading you into having a weaker Chapter 5. We can't know for sure until the game is pretty much finished but I like to explore what can be gained from compromising some minor things.
I actually don't even think much about the post-war investments when talking about chapter 3, it feels like more of a chapter 4 prelude than anything and it is hard to talk about what "perfect investments" look like for now, but I think the best way of looking at it is that you have the obviously great investments you shouldn't pass on and that most optimized routes can afford (the 3 new country trades, Min trade, Yhilin trade, Eustrin guild) and then you need to see what else you can afford, which I rank like this:
Can afford a social investment OR mushrooms: bad
Can afford a social investment AND mushrooms: decent
Can afford gasm falls trade: good
Can afford gasm falls trade PLUS one of the remaining investments: incredible
Of course even a "bad" post-war investment sections can still maybe be a good route overall, like it is the case for most 3 banks routes, it is just a matter of being able to make up for it.