I'm still holding on until the second part of the Ardan crisis happens before I try to optimize chapter 4 and 5 investments, but I had some time to play around with the calculator and wanted to exhaust some investments routes heading into chapter 4. Before I get to the routes themselves I should probably contextualize how I feel about certain variables and investments:
Deeds of Vinario: The stats are not great even if it is a unique opportunity, and the 100k from not investing on it could be put to good use. I personally think not having the deeds could backfire in the future, but that's speculation and it would be silly to not analyze the potential benefits of skipping this investment.
Sanitation Mages: Very similar to Deeds of Vinario, but has meaningful impact on the Tak'Kan vote during the Synod. I hold the opinion that even if it meant missing the "Tak'kan Major" result during the Synod, it could maybe be worthwhile skipping the sanitation mages, 400k ProN in discounts is not that massive and the stat benefits are even worse than Vinario's. However, "Tak'kan Major" could have more impact in the future and early sanitation mages could also have an impact on the Ardan succession dispute, so I didn't experiment with it much since the early benefits are very similar to skipping Vinario.
Mercenary Flotilla: Bad investment, can be made viable if used to get the extra discount on the Ardford bank, but honestly it is probably only worthwhile if copying Ghanth's aide turns out to be a bad idea.
Army Size: It only plays a tiny role during the Erosian War at the end of chapter 4, and the game repeatedly states that normal armies will be even less useful in the future. I personally think that army size might still play a role in the future but it won't be a critical one, so while I acknowledge runs that manage to finish the 3AW with 175+ army size, I don't give it much priority.
Trade Negotiations: At this point we are sure the RP gains from the best result are completely superfluous, so the second best result is just as good and taking the Northern Site to get extra Victory Points is valid when needed.
Discretionary Funding: I'm always willing to skip the monastery renovation until chapter 4 if needs be, this gives me 25% DF for clean-up stuff which opens some avenues for how I prepare for the Battle of Yhilin.
Research: I always take Orc Development first instead of Essence Shielding, it is what gives me wiggle room to play with the investments before the Battle of Yhilin, and I don't think the 4k exp missed by Simon not being in the Unforge battle will ever be relevant.
On to the routes themselves:
3 Banks - Skip Premium Steel
This route is not a good one, but I just wanted to have it as a proof of concept. By cutting corners with the small Yhilin investments, I manage to get all 3 banks and the important "political" investments in Ardford. This ends up costing me 2 Ginasta RP from not having enough RP with Janine and some army size. Worst of all though, I'm super broke in the post-war investment phase and so I could barely afford any extra investments then, in this specific save I even took the shrine during chapter 3 just so I didn't have to spare 25k for the aid station but still get the Gasm Falls Shop in the first chapter 4 iteration. I could have played with it more to avoid that but even financially it is pretty weak for a 3 banks save so I left it at that.
3 Banks - Skip Vinario
This route is very similar to the previous one, but by skipping Vinario I can afford Premium Steel, which in turn lets me get the Gasm Falls Shop during the post-war investments, arguably this could financially be the strongest route I have to start Chapter 4, although it has some of the same drawbacks as the previous one. In terms of returns theoretically it would eventually fall behind due to not having the Crystal Refinery, but one could make the argument that picking up the Crystal Refinery after the Erosian war might not even be financially worthwhile with there only being so many investment rounds left, also having the Yhilin bank right away gives a great early boost to the profitable chapter 4 investments.
2 Banks - Mercenary Flotilla - Skip Premium Steel
Note, I did not have to make as many concessions as I did to make this route technically possible, but by cutting a lot of corners I managed to have enough money to pick 2 extra investments in the post-war investment section, sadly I still couldn't afford the gasm falls shop. Aside from the drawbacks previously mentioned like less army size and -2 Ginasta RP, this route also can't get enough Yhilin acceptance in time for Yarra's lecture, so I only get the Succubus Pin instead of both it and the Sexual Pin, that's a concession I'd be willing to make but it is worth pointing out.
2 Banks - Mercenary Flotilla - Skip Vinario
Of course, skipping Vinario and getting Premium Steel makes the Mercenary Flotilla route much more viable, I don't have to cut corners for the Battle of Yhilin and I can afford the Gasm Falls Shop in the post-war investment section. It is still not a super strong route in financial terms, but it isn't too bad either.
2 Banks - Default
So by going 2 banks and not stretching myself to shoot for the mercenary Flotilla, it is easy to get everything perfect for Chapter 3. I had a close call being able to afford the Gasm Falls Shop in the post-war investments, in this route I chose to simply not do the monastery renovation even though I could, this gave me enough money from the DF leftover so that I could get the Gasm Falls Shop. I could have gotten the money through other means like skipping Dusty Horde and sacrificing some army size, or skipping the Ardford Restaurant investment, but I chose to go with the method I mentioned.
2 Banks - Default - Skip Vinario
So this is basically the same route as the previous one, but I skip Vinario just for greed and it enables me to pick another extra investment during the Post-War investments on top of the Gasm Falls Shop. This is probably the second strongest financial route, behind only the 3 banks one where I also skip Vinario.