If using the plumbing drawings, I find they help on some but I really like the interactive "parts catalog" better when on newer RV (after 2010) as it lets me get a better look by turning and zooming, etc.
https://catalog3d.winnebagoind.com/menu/Parts.htm
If I'm reading right? Correct me if wrong!
If there is no leak with black valve closed but it leaks when opened, there seems one big suspect but not an easy one to get to it!
Click these snips for better view or go direct to see what I'm looking at for suspects and location?
It seems like overfilling, etc would just go up the vent pipe? The stool is not an option to relieve pressure due to RV sealed. But if it didn't, then we have to move on!
One point where we might get a leak is the seal under the stool or at the vent pipe. But as you mention, it only leaks when the black valve is opened, that says not those points!
But there IS one joint which is listed as rubber, therefore more inclined to blow out. It would also fit what you say about leaking when black drain is open but not when closed!
Side view
Bottom
For getting to this, I doubt there is any ready made access. Do you have a firm layer that might be call Coroplast(?) under all the RV? A type of foamboard?
I might want to go under and run a wire up through the foamboard to feel and find the edge of the tank and line up with the main drain outlet to make an opening under this joint?
Or maybe just start with taking a way big chunk out to give plenty of room to work???
It looks like a bummer but maybe it will help to get a better idea of what's hidden in there? Best of luck as it doesn't look like fun!
I'm always interested in reports if this works out or not! Much of the remote repair theories are just pretty close to "best guess"!