Upgrade from 600D
The 7D and the xxD APS-C camera bodies all have superior ergonomics over Canon's Rebels. The 7D and xxD controls allow you to set up the camera and shoot faster than the xxxD bodies. I prefer that capability myself.
You are correct that if you upgrade to a full-frame camera (1D, 5D, 6D), you will no longer be able to use your EF-S lenses and you probably won't be very happy until you replace all of that zoom range that you already have and use with your EF-S glass.
There are plenty of people in the forum who will tell you that full-frame is the only way to go. I won't tell you that. You can get great photos from APS-C cameras--better than you could ever get with 35mm film, even Kodachrome. You can certainly get better photos with full-frame digital SLRs. I cannot argue that point. You can get even better images with medium-format digital cameras that cost the same as a luxury car. Only you can decide if you're a good enough shooter to take full advantage of a full-frame camera body and if it's therefore worth the added expense.
Now for 7D versus 60D. If you shoot birds in flight, you might well prefer the faster and more sophisticated focusing ability of the 7D, although I get the sense that it can be finicky. I've seen lots of posts about having to learn to use the 7D's more sophisticated autofocus. The 60D's focusing has been easy to learn in my experience. If you're shooting birds on a branch or on the ground, then either camera will get the shot.
I have a 60D. I already get nice shots but it will be years before I can say I've mastered its complexities. I waited 7 years to upgrade my 20D to a 60D and I would not buy a 10D when it first appeared because it could not replicate the responsive feel of a film SLR, so you get the idea of the type of photographer I am. You might or might not be like me.
Shooting with Canons for 40 years