I think the hose idea is a start--if the vent is straight into the tank....I would send the hose down first open-ended and see how far you get, open the gray tank drain and then start some water thru the hose and see if it comes thru. Would not force any water thru until last resort--might cause a problem that would require more tearing apart in the basement. If you get water coming out the tank drain, then the vent pipe is ok. If water doesn't come out the drain, then there is a blockage above the tank. If you get water to come out, then the problem is somewhere between the sink and the vent pipe?
Sounds weird, tho. Hope you get it figured out.
2016 Tiffin 40 QBH
2015 38RSSA, traded
2005 TK3 #1869, 10 yrs of memories,
2017 F450 KR--one more Ford is it
2009 F450 4x4-died; 2010 F450-retired