After using VG only for a few months, I am pretty much certain that PG is not the issue for me. My eczema comes and goes but only in one or two small patches at a time. I won a small bottle of e-liquid in a contest that must have a fair amount of PG in it based on it's viscosity, and after trying it a few times I haven't noticed any particularly bad effects from using it. Since I've stocked up on VG juices I don't have any good reason to switch back to anything with PG in it. I'm missing out on a large portion of flavor concentrates for DIY and the juice vendor availability is sparse to put it mildly, but I'm finding enough PG free options to keep me vaping.
I still don't know the initial cause of my eczema, but I have found good ways to treat the symptoms. Sarna, a steroid free anti-itch cream, is fantastic for itch relief. Keep the inflammation clean and moisturized when possible, and don't scratch. Inexpensive hand lotion is working as well as anything else. If the skin is broken and/or weeping, anti-biotic ointment and gauze pads or other bandages heal the area quicker than anything. Don't stop treating the area until it looks 100% "normal".
I'm not a doctor but even if I was, this is only what has been working for me. The main reason I started this thread and kept up with it is to let other e-cigarette users know about my experience with a coincidental outbreak of eczema and my initial use of e-liquids. I can only guess how many users have blamed health issues on vaping, but there are a few people that really can't use PG at all. Vaping isn't for everyone, but after failing at every other method to quit smoking I had to try and make it work for me, which it has. I'm already past the 6 month mark, and looking forward to my 1 year cigarette free anniversary!