Best approach to optimize FB campaigns when CPA is very high ($100+)?

It sounds like you're doing a lot right. The biggest thing I would suggest is to adjust your account structure to retain learnings within campaigns.

Your example of taking a high performing Ad Set and adding an Ad to reset the learning period caught my eye. In a case like that, you could instead keep the high performing Ad Set running, duplicate it and add whatever new creative you want to the new one, and use Campaign Budget Optimization to maintain your hard-won performance while allowing it to evaluate your new creative.

But the principle that's based on is keep Campaigns live whenever you can, use CBO to your advantage, and add instead of change whenever possible so you retain your learnings for as much of your spend as you can.