What is the best foam board insulation under drywall

I think that’s a fine plan. We really like mineral wool insulation for the fact that it has high recycled content, it handles incidental moisture far better than fiberglass insulation, it has a higher R value per inch than fiberglass and it’s a good for soundproofing. You’re right about polyiso insulation and its reduced performance in cold weather, you may have read that here but we do have a page all the different options for rigid insulation –

Rigid insulation panels: which are best and where to use them

While most insulation materials actually perform a little better the colder it gets, polyiso is the opposite and its R value tends to drop when it is exposed to cold temperatures, which is not a characteristic that is what you would call ‘appealing’ about insulation, that it fails you when you need it most! In reality it still works, just not as well as the manufacturers may claim, and it isn’t a catastrophic drop. But overall we do like it, since it has a higher R value per inch that EPS, yet it uses blowing agents with the same GWP (Global warming potential).  But in your case, the way you would be installing it is perfect, on the interior of the wall where it will stay much warmer and perform optimally. So I would say go for it.

And there is another big benefit to using polyiso rigid insulation panels on the interior as you plan, it has a built-in vapor barrier with the foil barriers on either side. So you wouldn’t need to add a 6-mil vapor barrier afterwards, you just need to tape the joints. There is some evidence of panels shrinking, so to be safe I would go for a higher quality tape than the standard rolls of red tape you will find in building stores. Something with a better adhesion and a bit of flex will help to ensure an air tight seal.

One thing I would point out, is that for the effort of going around the house with all the rigid boards, is that a 2 inch panel instead of 1 inch would boost your wall performance by somewhere are around 20%, but that's only if you can spare the space.