I'm mostly concerned because I have only 4 points of Anti-Lock and 9 points of Anti-Despair from my team. Is it possible to stall for 20 turns without any Active Powers?
If so, then I'd be able to fire off a Marco for full heal, Garp to get 2 Yellow Orbs, Doffy to boost + move them on Garp + Friend Captain Marco, Rakuyo for Yellow Orbs on himself and Captain Marco, Impact for the boost and then do burst him down.
I can't speak for certainty, but I want to say no.
The problem you'll face is there isn't enough no damage turns for stalling to begin with and this goes for any conventional team, outside of a fully optimized Sengoku team. Worst case scenario with unfavorable turn counters from the videos I've seen, the low end for no damage leading up to the boss is a minimum of 9-10 turns. I personally haven't watched any of the WB runs, but those would be your best case studies to look at where to take damage.
However, your biggest problem is HP and keeping your captain ability active. You'll need to take damage in Stages 1-2 to some extent and even if you managed to fully heal by the time you get to Stage 3, your lack of Lv1 lock/silence will definitely kill your run. You need damage output to clear that room fast, or at least in two turns and still somehow heal in your case. Something to keep in mind the big units there hit for 6,000+, while the marine that puts the lock/silence on you I believe does ~4,000 damage.
Your hypothetical situation is:
- stalling 20 turns somehow in Stages 1-2
- survive and fully heal by the start of Stage 3
- take damage at Stage 3 due to lock/silence
- full heal again, clear Stage 3 room
- clear Stage 4 room immediately with no damage
- 3 turns to burst Aokiji while farming PSY orbs
Don't put too much weight into OTK Aokiji would be my recommendation. A 2x Garp, Garp/Shanks, Garp/SW Shanks team would work just as well, with subs of Marco, Impact Usopp, Rakuyo and Doffy. Your goal shouldn't be to burst him in one turn, but get him to 50% within 3 turns then burst the last 2 million HP. Remember Aokiji only does damage for 80% of your health for his first attack.
In this team setup, you actually have leeway with Marco being replaced as a sub and can bring GP Usopp for Stage 3 and beat that room with ease. Or if you prefer, bring a damage reducer like Alvida or Mirage Nami for Aokiji for more turns to chip away at his health, or story Enel, as a secondary PSY booster. There is a bit of a misconception of what runs are fastest too, just because you stalled say 10 turns before you got to Aokiji and OTK him doesn't mean your run will be as fast/or faster as stalling say 7 turns leading up to him, and another 3 at him while killing him. You definitely have a team to beat the up coming 60 stamina, so that isn't a concern at all.
The rule of thumb for Aokiji is, if you have Lv1 lock, Lv2 silence then bring your orb + type boosters. If you don't, then bring a delayer and/or damage reducer or offset things with a lot of HP.