Looking at the walls in my walkout basement (NH, zone 5), I noticed that I have a mold problem developing. The house is about 8 years old. One side of the basement has regular poured concrete walls, the opposite side has only a 1ft knee wall with 2x6 framed walls on top (and the side steps down). There is no insulation on the concrete, the stud wall is comprised of vinyl siding, house wrap, plywood sheathing, R19 fiberglass, poly vapor barrier. The vapor barrier is very poorly applied (stapled occasionally, gaps on the top / bottom and in some other places).

This wall system clearly doesn't work well. There is some evidence of surface mold on the outside (fiberglass side) of the poly, which I suppose comes from humid air making it inside in the summer and condensing on the sheeting (it stays ~ 55 degrees in the basement in summer). Worse, there are also some stud bays where the plywood sheeting is starting to develop mold -- this seems to be correlated to me seeing frost on the inside side of the sheathing as I open up the bays (the picture below shows the worst I've found so far, most bays are just fine). I believe this is interior moisture making it across the poly, through the fiberglass and condensing / freezing on the sheathing. When it gets warmer, the ice will melt, the plywood will get wet and I suppose that's where the mold comes from (and maybe directly from condensation). Fixing the poly sheeting might help with the winter problem, but it also should make the summer issue worse.

I also want to finish this basement eventually, so I figure I should fix this right. My plan, which I started to work on is the following, a couple of stud bays at a time:

Remove poly, fiberglass. Many bays look fine, but some have frost and/or mold. After removing the insulation, the frost melts and the sheathing dries pretty quickly. I clean off the mold (soap and water), and I put some hydrogen peroxide on top. Glue 2" XPS into the stud bays, fill the gaps with spray foam. I have a bunch of kraft-faced R13 fiberglass laying around, so I plan to put this on top of the XPS to fill the stud bays. I'm wondering whether to leave the kraft facing on for now, since I won't be putting anything else on top, though I realize that I have to put something (e.g., drywall) as fire barrier eventually.

Does this sound like a good plan? I want to, eventually, cover the concrete with XPS, too, and frame around it.

Is kraft-faced insulation on top of XPS okay for the time being?

Is it okay to put XPS on top of the sheathing, even though some mold may still exist? It seems to me that because of the XPS, spores shouldn't easily be able to make it indoors anymore, and because the moisture problem should be fixed, the mold should stop growing / not come back, though it won't be possible to verify that because it'll be under the XPS.