It is fine to travel with a full tank. That is what they are made for, and are designed to do it. 95% of my camping is boondocking, so I have to carry a full tank. It's never been a problem. Do a search on all the different RV forums and see how many people have had a problem caused by a full tank. Good luck, because you won't find many actual problems from it. Just lots of people who are afraid and don't think you should, with nothing to back up those fears. There is a lot of engineering that goes into the size and placement of these tanks, as well as how they are mounted. Fill it up and fear not.
Becky, Bob and Taylie & Bode
2009 Silverado 2500HD Duramax/Allison
2014 Heartland Sundance XLT 245RL