Have you checked the main Classic & Vintage forum? Lots of us share your "disorder"!

I'd recommend keeping the bike and adding to your collection. We refer to the syndrome as N+1. And I don't see anything wrong with tinkering as therapy. I think it's perfectly human to want to stay busy.

In my experience, gel padded saddles can cause more pain than a hard saddle. Try one of the modern favorites: Fizik Aliante, Selle Italia SLR, or some classic favorites: San Marco Regal, San Marco Rolls, Selle Italia Turbo, or my all time favorite: a Brooks leather saddle. An inexpensive sleeper classic which I can recommend, and which has more cush than the above, but not too much, is the Avocet Touring I or II. They can be found on ebay periodically.

But often, with a saddle, it's really a matter of the rider's backside "breaking in" rather than the saddle!

Is that enough unsolicited advice?