Need help wiring Tstat

So I have a standard a/c system wired to one thermostat (lenox 51m34) and my 2 wire gas furnace wired to another. I'm trying to consolidate them onto one thermostat. Ran new wire to replace the knob and tube to the furnace, but now can't seem to get the furnace working correctly with the lenox stat. Using the old stat, it seems that I get 24v from the red wire from the furnace, which is just jumped to the white wire when there's a call for heat. For some reason it doesn't work when I connect the R from the a/c to the stat (leaving the R from the furnace disconnected). It doesn't work at all using the lenox stat (I haven't tried changing any settings on that though, so it may be set for a heat pump or something that behaves differently).

Anyways...

The plan is to use this stat. Not sure how the wiring should be though. Any thoughts? I don't see why I can't just use the R wire from the a/c unit and the W wire from the furnace. Only weird thing is that seems that I get 28v from the a/c (between C and R wires)...

I only have a common from the a/c system. Perhaps I need to use the Rc and Rh terminals?
Edit: Crap, just looked at the manual for the motison, and it doesn't have separate Rc and Rh terminals...
I still don't know why I need both R wires if the only function is to provide 24VAC...