Thanks to all!
The salesman brought a tech guy with him, who did look underneath and peaked under the plasticized cardboard. When he replaced the screws, he pounded the bottom and said that that was the sound of dryness. There is nothing wrong with my tanks. They simply expand a bit when full and give the appearance of sagging. The salesman admonished me to always call him first, because I am still under warranty, and the first guy I talked to was wrong about almost everything. There should have been no cost for the on-site visit since I was within 5 miles of the dealership.
The black tank smells a bit outside when full, but that is solved by dumping it. It's the vent, not a leak. He agreed that shutting the grey tank and adding Clorox was a good thing, because sometime grey water finds a place to sit and stagnate.
Thanks to everyone who offered advice, and I'll be using much of it in the future. It all lined up with what the salesman and the tech guy told me today. I gave them the name of the first guy who gave me such a hard time. They were a little upset with him.
Before I got old, I thought having an actual tent instead of just a tarp was luxury camping. I'm enjoying 25' travel trailer.