My rig does the exact same thing as far as siphoning out the overflow tube once full. Water fill is gravity fed. I fill it until it starts coming out the overflow, then put a cap on the end of the overflow tube (I installed a threaded barb fitting). Once we take a shower or two I take the cap off, but it's not really necessary as the vent tube relieves any suction. We mainly boondock and this solution has worked for 5 years.
Scott and Liz - Southern NM
2012 Wildcat Sterling 32RL - w/level up (best option ever)
2007 Chevy 2500HD 4dr short bed Duramax w/allison
Reese Fifth Airborne air ride king pin coupler with Sidewinder