DirtySixer looks cool, but no way you'll get one for under a grand.
If you can find a used Black Mountain Cycles 65cm Monster Cross, it should come in under your budget. I have one and love it. Mike Varley, the designer of the frame is 6'3"rides a 62cm. I am 6'6" and have a 65 and can't say enough about how versatile these are. I have ridden it with 38,43 and 50mm tires depending on where I am going and it rides great.
If you are looking for new, check out the Fuji Jari in 61cm if you can find one. It's Claris, but you should be able to upgrade to 105 10 speed and stay in budget.
Fuji Jari 2.5