The opinions and observations below are mine--yours may vary.
Off the road again, and some more time to reply. So, I took a look at my latest remote and sure enough there are 2 nonfunctional, not labeled buttons, for a total of 12. I'll just call it the tstat of many buttons. I did not mean to imply that it could be installed by itself. The Dometic tstats are paired with specific control boards. In fact I am suspicious that the problems with the screwy fan speed switching by the few button remote is more of a control board problem. However, the many button remote and corresponding control board installed in our trailer by a competent AC technician running 1 AC unit does an excellent job of very narrow band temperature control with NO screwy fan speed switching. In addition, it is using the conventional tstat furnace control wire that the trailer manufacturer put in, quite well. It does not seem to need telephone wire. As long as there are 3 conductors available, it seems to do the job.
I absolutely agree that the tstat placement by the trailer manufacturers is terrible, and has a great influence over temperature control. But, in my case, the new tstat went in the exact same place as the old one--way up the hall behind the bathroom door when open. But the temperature control is night and day better--I have to attribute that to the many button tstat and control board. It is quite possible to have two problems--placement and the few button tstat. My experience with the few button unit was very poor temperature control and screwy fan switching--both solved by the many button and its control board. There are those on line who have absolutely no problem with the few button--not my experience with the OEM or a complete re-installation of tstat and control bd. To be clear in my case the equipment was a MUCH bigger problem than the placement of the tstat (which is still not in a good location).