Been through this one years ago...
I really got involved with a solution to the issue, and even contacted BF. That was before the demise and resurrection of BF. They provided no input nor help.
The black and gray are separate from the fresh water tank. There is not much in the order of support for those tanks... I will look through my archives and see if I can provide some input.
Draining both the gray and black are necessary... Fresh not so.
Removing the lower cover fiberglass cover will be needed. Then you can see the minimum support that BF provided for those tanks.
I did a fairly simple resolution to the problem but it does require some mechanical ability.
I did not post on RV.net regarding this issue...
I will pm you for more information...
Jim