I havent installed the American Standard Champion so first hand knowledge I dont have. I did inquire about this toilet at one of the plumbing supply houses I use though. What they said was that they are getting quite a few complaints/returns with these toilets. Like I said, this is second hand info, but they're the ones selling them. I'm sure others on this forum have been installing them. Perhaps they've had better luck with them.
Have you considered one of the Toto toilets? If you're looking to spend about $300 many of the Totos fit into your budget. You might want to take a look at the Toto Drake. Its a great flushing toilet.