We too have a 2350 with the gray tank being the smaller 23 gallon one. Given we almost exclusively dry camp, the gray tank always fills long before we run out of fresh water. To buy time, (per Phoenix USA instruction) I flood the gray water into the black tank by first opening the gray tank valve, then the black tank valve, wait for the gurggling sounds to quiet down, then close the black valve, and finally the gray valve. I usually do this once between every fresh water fill-up, so it is done very frequently during trips. If getting very close to empty with the fresh water tank, sometimes I have to do it twice before dumping. It is no big deal. Only an inconvenience.
Given we don't do #2 in the bathroom, without fecal matter to be concerned about, I am tempted to keep both valves open all the time, but worry that if sewage ever did back up into the shower pan for any reason, it would be contaminated with urine. It does seem a remote possibility which has me tempted. Also, I think some rigs of other brand motor homes, have the shower pan dumping into the black tank.