I don't think that a $1,000 amp is a waste on K701s if you like the sound - the K701s are as amp-dependent as any headphone out there, and the fact that they are $270 is, to me, irrelevant - they perform as well as anything up to the $500-600 range, and you should treat them as such.
For $1,000, the Burson seems like a good bet that people like a lot with the K701. A Woo WA6SE would also be an excellent match. And given what I've been reading, I wouldn't be surprised if the Lyr was also excellent.
If you love the K701, I think it's totally reasonable to build a strong system around it. I was a very happy K701 owner for a long time, and still think it's an outstanding headphone for the price.
That said... I wouldn't argue with the folks in this thread who say that $1,000 on a Stax Lambda rig would also be an excellent use of your funds. I got an excellent deal from a friend, $500 for a vintage Lambda normal bias and SRM-1/MK2 amplifier, and sold the HD800 I was using at the time - those Lambda rigs are really outstanding, and I'm sure you can get a used headphone and amplifier for much less than $1K if you're willing to buy used/vintage.