I think the OP made it abundantly clear the WANT an onboard W/D...they were asking what kind?
There are other options other than Splendide...we have Whirlpool stackables that work great. We full time and I wash usually once a week, four loads, easily handled while puttering around the house.
As far as propane, I've not seen anyone do this, but it should be possible, as it usually only involves changing the orafice for LP instead of natural gas. In our rig the W/D is directly above the propane tank so it should be fairly easy to run the line. If you go this route let us know how it works out.