T63 is pretty awesome for the offroad bits, but they wear quickly, cup, and run hot on pavement. They are my tire of choice for the KLR, but it doesn't see much dry pavement.
If you aren't playing in the mud, I'd look at the Shinko 705 and Full Bore Adv tires. Smoother on the pavement, enough tread for everything else, and better wear. If it helps, I've run BT003s in the conditions you listed on my 'tarded DR, the muddy sections were, ummm, fun(?), but otherwise, they offered a tolerable level of traction offroad.