Finally, some success! Of course, still lots of room for improvement but it's something. With LOTS of make-ready and way too much time, I've been able to print first colour of the first 58 of 100 Save the Date cards. Why 58? Well, I bought lots of really lovely textured paper to use, and a few sheets of stuff I thought would be nice to have on hand. The nice stuff (Rives) is actually heaps better and very similar to Crane's Lettra, so I've decided to use up what I had and buy more tomorrow morning.
Seems that all of my problems definetly were the base, and I'll still need to think of a long-term solution, but for now, I'm happy.
Oh, and I bought a cheap corner rounder as well. If I do a lot of rounding, I'll need to buy a better one. I'll be rounding these cards though, it seems to work well with the design.