I had a similar, but less severe, problem when I used to paddle every day. I was living on the cheap, and didn't want to shell out for a new dry top. Solution: safeway bag. Before putting my dry top on, I'd poke a hole in the bottom of the bag, slip my arms through the handles, and put my head through the hole--a very strange neck-vest. Once the dry top went on, I'd situate the shopping bag as a liner, so the latex didn't touch my neck. If I was feeling stylish, I'd tuck the shopping bag under the gasket cover so it was invisible. If I wasn't feeling stylish, I'd get a lot of comments. The upsides: effective, dry, cheap, and a great icebreaker. The downsides: I'd still touch latex getting the top on and off, and my wrists were still exposed. Wrists were probably OK due to my Travolta-like abundance of body hair. Thinking maybe you have a little less of that, Brenda?
Sounds like you're far more allergic than I was, or in retrospect, maybe I just had a really bad chafing issue. But take it for what it's worth...