I have four solar panels on the roof of my TC. They do a great job charging the batteries every day. To answer your questions:
Can I add a solar controller and panels that will charge my batts without worrying about any ill effects to the converter being affected? Does the solar back-feeding the converter cause problems? No, your converter will just sense a higher voltage for the battery/solar controller combination.
What type of panels are the best to get for a camper roof? What do people use to install them through the membrane and prevent leaks? Any particular concerns about drilling through the membrane? I installed basic Renogy 100W hard panels. When I began installation on the roof of my new Northstar, I contacted the factory for advice. They use Eternabond tape between the solar panel foot and the TPO roof material, screw it down, then apply Dicor self leveling sealant over the screw, solar panel foot, and Eternabond. I used double sided Eternabond tape, it sticks to the roof and to the foot.
Where is the best site to learn more without getting into a full-blown solar zealot approach to state of the art solar power generation involving thousands of dollars? The best I found is DIY RV Solar Systems Facebook Group. Lots of great ideas and examples of small to immense RV installations.
I start talking about this and my wife's eyes begin to glaze over almost immediately. All she imagines is a mountain of cash going out the door. Yeah, just wait. You will have anyone you ever talk to glazing over and walking away. "Hey Joe, you should have seen yesterday my batteries were pretty low, and I was getting 22 amps from the solar panels!!! Never saw it that high!!! Wait, let me check it right now. A little lower today, must be because the batteries have more charge in them. As I was saying, yesterday... Wait, where'd he go?"