I remodeled my kitchen from a separate room to half walls looking into the dining room and living room. This created a problem for the vent stack. The wall containing this stack was gone. I installed an AAV as high as I could in the half wall behind the sink. I also have the dishwasher draining into the sink tailpipe. When the dishwasher drains it backs up into the sink. The sink drain is also quite slow. What can I do to make this situation better short of running another vent line in the floor connecting to the bathroom vent?