Like @phoenix, I think you've overly restrained yourself by forcing the build to include simultaneous levels as an advancement. It (and the build-up techs like additional AP) has a pretty poor return per AP invested.
Additional AP's impact is easy to quantize: it's +25% (23% for you, though I'll do 25% for easier math), with no added effort. One level of simultaneous AP is +100% in optimal scenarios, with some additional effort. So, the net result is at most +150% AP gain, with a direct cost of 7718 + 13,301 = 21019 AP. Plus all the extra Phase 3 (and phase 2, to an extent) spent to unlock simultaneous levels in the first place probably puts the true cost closer to 40K AP.
For a baseline, I would say a low-effort player will want to check in at most twice per day (once in morning and evening), perhaps 3 times so they don't have to think about it the rest of the time. That means they are only progressing 4 or 6 hours per day with no additional idle time. If you put 1822 AP into increased idle time, that gives 8 hours total, leading to 16 or 24 hours per day, which is a +300% or +200% gain already. I'd consider going all the way up to 12 hours total idle time for 4542 AP to minimize effort.
Another way to find likely higher return is to look at what do you need to do to beat a level. You need to generate some number of armies from army camps, generate some amount of money to upgrade things and buy mercs, and possibly wait for hospitals to upgrade. We can speed up the army camp generation portion of this by +200% for just 1930AP, we can pretty reliably get infinite effective money in 5.14 with +100% alloy sell price (1756AP) and -50% merc cost (1002AP).
With those components taken care of, the only question (which is the same for both low and high-effort strategies) is what fraction of your armies are going to come from camps versus caches versus hospitals versus mercs. Due to the use of auto-conquer and lack of investment in late-game techs, caches will likely only give their base of around 10%, joint strike maybe 10%, hospitals maybe 20%, and base mercs 15%, so you are missing 45% of the armies as a baseline. You can get half of that (22.5%) from additional mercs with no extra effort and 16630AP. For the rest, you either need to play more efficiently (hard without effort), take some in drafts (some effort, though reduced by Increased Draft Sizes advancement), take the increased army cache size and better hospitals advancements, or wait for army camps.
As a concrete counter-proposal, that doesn't bother with any phase 3 or 4 advancements (and could easily be optimized), I would suggest:
- 25% auto-conquer (392AP)
- +10hr idle time (4542 AP)
- +150% additional mercs (16630 AP)
- +100% alloy sell value (1756 AP)
- +300% IACP (4380 AP)
- +300% draft sizes (3405 AP)
- -50% merc cost (1002 AP)
- 20% auto-upgrade army camps (1051AP)
Total: 33,158 AP
There's enough leftover you can still grab +25% additional AP here too, even.Alternative view
With 5.14 markets, the least amortized effort might be to pick a few levels you know well, learn the efficient paths to beat them, then play actively every few days and don't play at all in between. You can easily beat high AP levels in < 1 day if you know where the hospitals, markets and a few key recipes are (probably not even required if you have 47K AP to dump between levels). This is more effort in bursts, but I suspect may net you more AP per effort in the long run due to how efficient gameplay can be right now if you know the levels.
Edited 9/19/2021 19:03:00