Thanks to both of you. I was pretty darned sure I didn't need to tape it; you've reassured me.
And the fittings in question are accessible, if that's the word, through either an access hatch that's 9" by 9" or the base of the closet (removing the floor) that's not much wider, but far enough down that only one arm reaches. So I'm not going to be changing the fittings out for anything else, just replacing the conical gaskets. Removing and replacing the check valves called for 1/2" drive tools, and all the fancy stuff I'd collected over the years: universal joint drives to let me angle the foot-long extension, so I could apply the heavy duty ratchet - and so on. There's no reason that I can see for Winnebago not to have made the access hatch larger...grumble, grumble, mumble, mumble.