I just replaced my old mercury stats with the same Honeywell P'gramable stat.
My 24v system only has two wires.
The Rh and W are the only ones you need to have it run, assuming its heat only and hot Heat/Cool.
Check the transformer on your zone circulator and you should see only 2 wires attached..
This may be a late post. Let us know how it worked out for you.