I have a 7D. As the second half begins, always shooting around ISO 1600-3200 by the middle of the second half and 3200-6400 during the last 20 minutes. Using a Canon 70-200 2.8 v 2 with a 1.4 TC.
As the title says, a small problem, not a big one, but something to be addressed all the same:
The 7D is an APS-C camera, where both the 1DX and 5DIII are full-frame. (duh.) But you're already using a 1.4x TC with the terrific 70-200 f2.8 L IS, by which I presume you need the reach. On the 7D, you're essentially getting a 155-450 mm equivalent reach, compared to 100-280 mm on full frame. That's a HUGE difference. And even considering the extra pixels on the 5DIII, you're still looking at doing a LOT of cropping.
The 1D Mark IV was mentioned by a couple of posters. With that model, Canon made it's best APS-H sensor to date. And the 1.3x crop - a good compromise between full frame and the more extreme 1.6x crop of the 7D - provides a field of view equal to about 125-365. Of course, it's a 1D, which means awesome AF, rock solid construction, and speed that makes the 7D feel like a Pinto. The UI is very similar to your 7D, too. And the price won't cause you so much consternation. We don't hear a great deal about the 1DIV, I am guessing because 7D sales cut into it on the speed side while the 5D-series cut into it on the IQ side. But it's an amazing machine that will likely exceed your demands without exceeding your budget.
Best of luck
ps.
By the way, since this post discussed the issue of cropping, teleconverters, etc., it might be worth pointing out that the 70-200 EF 2.8 L IS is actually good enough to sustain a 2x TC without a signficant hit in optical quality. Speed MAY be an issue, but a fast body with a huge battery pack and dual microprocessors like the 1DIV and 1DX can probably cope just fine, offering a field of view of 180-520mm and 140-400mm respectively... and at a constant f5.6 max aperture, too!