In order to utilize a separate heating (rh) and cooling (rc) power source you must use the learning thermostat. You are right that the basic thermostat model just doesn't have enough terminals to do what you need.
Is one of the R wires a jumper? Hard to tell from the picture. If one is a jumper, just use the main red wire coming up in the main thermostat wire bundle and connect to your R terminal on the new base. No need to use a jumper on Nest stats for Rh and Rc as both are connected internally through terminal R to run both heating and cooling. Hope this helps?
That is a strange thought and made me look real close, good catch sakrue... it looks like there's the default bare silver jumper back behind there. It's strange that they'd connect heating and cooling power together unless they both come from the same furnace.
I guess more info is needed. What's the source of heating? Is it a separate boiler or forced air furnace that's shared with the a/c blower?
I wanted to reach out and follow up. Please let me know if you are still having trouble wiring the device, as I will be locking the thread in 24 hours due to inactivity.