Well, I am happy to say we’ve solved the issue, and for you all who were kind enough to reply, and for others in the future, I thought I’d let you know what we found.
Hubby checked the black tank vent as many people had recommended, using a plumbing snake, and it was totally clear. He checked the toilet plumbing and even replaced the valve (while he was correcting a bad installation of the toilet), and it was still happening. We hooked up to shore water, still happening. I listened again and decided maybe the location of the sound was actually the water heater, which is on the floor of the closet right next to the bathroom, on the side where the noises were coming from. Hubby got down and watched/listened to it while I flushed and VOILA, that’s where the noise was coming from. Seems the bypass valve that is used when winterizing had some sort of small blockage? We aren’t sure, but we had both seen a YouTube video of a guy with a plumbing noise problem in his RV who discovered that his bypass valve was not fully opened, and when he fully opened it the sound went away. Hubby had already checked that valve, but he turned the valve lever back and forth a few more times for good measure, and poof, the problem is gone. We really aren’t sure if there was a little debris in there or what, but we know there was debris in the toilet valve itself, as he replaced it and found debris in the screen.
At any rate, the horrible growl/groan/flatulence sound is gone and we can flush in peace now. Thanks, everyone, for trying to help us trouble-shoot!
