You could buy older Ultegra stuff -- 6600 and 6700 are both 10 speed; the 6700 shifters have the cables routed under the tape. You probably won't have to pay that much for it, and you'd be able to run your current crankset, cassette, chain and brakes. You also of course wouldn't have to worry about changing your rear wheel.

Also, of course, you don't have to stick to Ultegra if you want to move to 10-speed Shimano. 105 and Dura Ace, will also work, and you can mix and match. Lots of options. If your goal is to switch how your shift levers feel, I'd look at 10 speed Shimano.