To pull back the towel just a bit, the grey tank plumbing could join prior to the valve since they both serve the same function. This would allow using only one valve. IMHO, the only way to be certain would be to check the plumbing.
My experience has only been with older RVs, three starting in the late '70s. With them fresh and holding (black+grey) capacities have been fairly close. You appear to have more than twice the holding capacity than you have fresh water. I would wonder why there is that much extra holding capacity if there is nothing on board to fill it. Again, If it were me, I would verify these numbers.
We usually have the fresh water and water heater filled before leaving (unless I forget). It does make a difference.
I never have, but I have friends who carry several 5 gallon jugs of extra water. I've also read on this forum about folks with 5ers and TT's who added large fresh water storage in the beds of their tow vehicles for extended boondocking.
Throw towel back.:-))