Bear with me on this story. I believe the above "recommendations" are wrong. Simple reason is you need to have a complete circuit as you stated. I purchased a Honeywell RTH6500WF for installation. Much to my surprise, I found out you had to have a "C" terminal. The HON adviser stated I needed to add an additional 24 volt transformer - which I did, a HON AT72D 1683. I ran it off the 120V for the furnace so that it is off when the furnace was off. Heat and wireless worked great. That was a year ago. Summer came. I turned it to AC and had nothing. The "fan on" also never worked. Using the "R" from the furnace and touched it to the "G" and the furnace fan went on. Touched "R" to "Y" and the outside condenser went on. Problem is in the HON Thermostat!
So I call HON again. Seems that they are not really focused on helping us DIYers. First adviser said he could only help me with programming. Electrical work must be done by an experienced HVAC person. I understand, but I NEED AC. So hung up and called back. Next adviser said basically the same thing. Have your HVAC person add a "C". I said I have a "C" but where does the "Load" or "R" connect. Sorry cannot help you.
So we moved to trial and error based on various videos on U-Tube. The HVAC call out fee is 250 USD so it is more than a new thermostat and it is only 24 V. So here is what I found. The "C" lead from the added 24 volt transformer goes to the "C" on the thermostat base. I then to the "Lead" or "R" from the added 24 volt transformer to the "R" block. I hooked the "R" from the furnace and hooked it to the "Rc" on the thermostat base. Nothing on the thermostat. (Hooked up the other way around gave me heat but no AC). So I said my prayers and found the jumper. I jumped "R" and "Rc" on the thermostat base and EVERYTHING WORKS. I have AC, manual over ride on the fan and heat. Good luck on getting your system up and running.