Having missed many years of running through Achilles issues and now being in a much better place I think shoe drop is interesting but probably a small part of the solution.

My walk around shoes are all zero drop. Because I figure why not encourage a long tendon when it's not under a lot of strain. If I could figure out a practical way to stretch them while I slept I would. When I was starting again I was putting heel raises in Hoka shoes because they are only 4mm drop and I was thinking take the pressure off while running. In practice I just stopped using them. No way of knowing if they helped or if it was the hokas or of it was the barryp slow and steady build up approach.

My suggestion would be to have low drop as much as you can and high drop in a situation when it's likely to get aggravated. But I'd also suggest maybe just avoid the situations that aggravate it. At least for a while. There is a great thread here somewhere (I'll find it for you) but the bit of advice it had which changed the way I think is that tendons like the right level of exercise. They don't like none (so don't rest totally if you can avoid it) and they don't like too much. It sounds like you might just be in the too much zone too often. So I'd say bring it down a bit until it feels better and then test it with the trickier stuff carefully.

ETA This is the thread I found very helpful.