So many questions so I'll try a few:

"Another thing that is turning out to be important is the interpersonal relationship with the dealer. Do those of you who buy on eBay care about this or is each transaction a one-time only affair?"
I guess this depends on how much $ you have to spend and what type of rugs the seller is offering. Usually it's a one time affair, but I try to 'get to know the seller' before buying (asking questions, requesting additional photos) this will give you a 'feel' if the seller is responsive or not.

"What sort of compromises do you guys typically make?" Spending a little more than I want to.

"And what elements are you not prepared to compromise?" Buying from someone who won't answer questions, too expensive of shipping, no returns, poor quality, major damage.

"Do you fall in love with a rug and use that strong attraction, even if not understood, as a touchstone?" Yes, there has to be some sort of 'attraction' for me to spend this kind of $$ (but I started out just buying what I could afford, I've now moved onto the next level, going for 'art').

"Or do you approach the search very rationally, with your precise needs (color, dimensions, budget) in mind, and searching for best possible apparent value?" Dimensions are very important (what if you buy a rug too big for your area?) Budget (I'll be eating Top Ramen for the next couple months), color and design are so varied it would be nearly impossible limiting these. Do research first...