Thanks for all of the comments and ideas
First, we really like the heat pump and would buy another rig with it (if I had the money). Because it uses the roof outlets to spew its warm air, all corners of the rig get heated evenly - not like the heat distributed by the LP furnace.
Secondly, I was in touch with Coleman and got a bit of help from them. The tech wanted to know if, when in elec heat mode, my blowers were working (both indoor and outdoor fans were operating), if the compressors were operating (they were) and whether there was voltage between the stat's Blue and white/black wires (the was - 11.9 v). He also admonished me about the low external temperature and room/set temperature issues in two messages . I know all about these concerns and had tried for 4 months to get the elec heat to work using every combination of Set, Room, and ambient external temp you can think of with no joy. Since I responded to his three questions, I was anxious to find out what the next step in the trouble shooting sequence would be. Alas, the next step never arrived because after I checked the requested voltage, the heat pump started to spew heat. All I can think of is that during the measuring process, I nudged a loose wire, set off some kind of current flow that reset something, or invoked the electronic gods. I advised the tech accordingly so I got no more help.
In any case, our external temp in Mission TX is 47F and the heat pump is dutifully keeping us warm..
Thanks again for everyone's input