Yep. My son has had issues with this since birth. Any PUL/waterproof cover, except all-nylon covers, do this to him. Bummis SWW were a big offender - covers with exposed PUL (Thirsties, SuperBrites etc) were even worse though.
When I switched to nylon, fleece, and wool covers, the rash vanished within a week or so. For out of the house, when PUL was really a good thing, I covered the affected areas with lanolin first (I wouldn't do this with a pocket or AIO with a fleece inner; just with natural-fibre diapers.
The issue for DS is, I have found, an issue of breathability. He can wear fleece next to his skin as long as the skin can breath - I have a couple of all-fleece pockets that are fine. So it's not synthetics per se that's the problem - it's air circulation.
We have found through trial and error that DS can tolerate a few hours in PUL every day as long as he gets lots of "breathable" time - so at home he's usually in wool or fleece, and out of the house we use Bummis Whisper pants/Bummis original wraps or g-diapers with a cloth insert.
Do you have wool or fleece covers you could try?