Why not try the Tricross with the Allez wheels? It wouldn't cost you anything but the time to switch the wheels and adjust the brakes, and it would definitively answer the question about how much the tires are contributing to things like slowness and comfort.
I love my cross bike (not a Tricross), but I haven't ever ridden a road race bike, so I'm curious about the comparison.
I feel obliged to note that cyclocross bikes are, by definition, race bikes. They just aren't road race bikes. You should try out cyclocross racing. It will help you develop a new appreciation for your Tricross. I know there were times last year where I just stared at my bike in admiration of what it was able to do.