Hi travel4family
You can avoid filling the gray tank by using the low ppoint drains and the FW tank drain. The advice to utilize the city connection is spot on.
As mentioned you do need to sanitize and then re-flush the system.
From the wording of your post it would seem the unit is in storage and inconvenient to mess with, correct?
You may benefit by modifying you winterizing technique. I use an ancient small 2 gal Craftsman air compressor to blow out all the H2O from the system. Drain the FW tank, bypass & drain the HW tank, and recirculate the pink stuff through the pump using 2 3way valves I installed for that purpose. That keeps the pink stuff isolated to the pump and traps which I fill as the last step. Once all the H2O is purged from the system you could restore the HW heater valves to normal and leave the drain open till spring. What little might drip into the HW tank will have plenty of room to expand & pose no threat to freeze rupture.
In the spring 2 gal jugs of fresh H2O pumped through the pump to the ground clears the pump. I then sanitize and flush as mentioned above and I am good to go. You could do this @ your first stop as you prefer.
1 Gal of the pink stuff does our whole rig with plenty left over even after I make a generous fluid seal over the toilet valve.