I am considering booking the Iberostar Tucan/Quetzal because of all the good reviews. However, there are some "horror stories" about guests who were bumped to inadequate hotels due to overbooking. How common is this and is there a way to avoid it? (like arriving early in the day or not booking with a charter group)

I don't think any resort is exempt from this. When we went to the Mayan Riviera last year we were bumped for one night from the Occidental Xcaret. Friends of ours this year were bumped their entire week from the Copacabana to the Sunscape Tulum (which was apparently a better resort). Perhaps talking with a travel agent to see how many times your particular resort has been bumped might give you a better idea, or email the resort prior to you leaving might be another idea. I think it also depends on when you go. During less busy times the resorts wouldn't be overbooked and this might not be an issue.