The only problem I've read about on the Roadie forums is that I'll need an Air Compressor to inflate the tire initially. Is there something I'm missing that is somehow related to the problems associated with tubulars?

Tubeless hase been working great in the mtb world for 10 years. There are obviously differences between mtb tires and road tires, but the limiting factor has been the tire beads ability to keep itself from blowing off the rim. The is apparently not an issue with the Hutchinson tubeless specific tires.

There are plenty of guys out there who run the tire for 3-4K miles (until it's worn) without a single flat. I want that!

To answer some of the other questions:

I'm on 23c tires.
110 is the reccomended max for the tires I currently have. Is it safe to go beyond this? On the cheap rim I have, can the sidewalls support the force of more pressure?

There are no burrs or anything on the tire or the rim. Te punctures do not happen in the same place (I align logos to valve stems) and are an obvious pinch flat. I still swear that I'm not ramming into things, but I know that'll be hard for most people to believe.