I have a 2010 29BHS and my furnace doesn't run with the A/C. It only runs on the heat. It appears that my thermostat (original analog) goes straight to the A/C and a separate wire goes to the furnace. (I don't have the schematics, just looking at the wires when I have cleaned the A/C filter. (or when I took apart the furnace at 9000 feet in the boonies on a 20 degree snowy night to remove a mouse from the squirrel cage
)(by the way that made a horrible shaking and loud vibration noise when the furnace fan started up)
I'd suggest you try flipping the power switch on the furnace to off and see if that will keep the furnace blower from running.
I just found a thermostat manual while reading another post
I think that because you removed your furnace that you are no longer supplying 12 volts to the thermostat which is required to send the signals to the A/C.