I will take 'em by the numbers
Q1) What are the benefits of going with a heat pump unit vs. a heat strip?
A1: It takes less energy to MOVE heat than to Generate it, so the advantage of a heat pump over Electric heat is a savings on electricity, over Propane it's a savings on gas. However you need both, because when it gets REAL cold out (Like below 35 (F) ) heat pumps.. SHUT DOWN if they are properly designed.
Q2) My system is non-ducted and does not have a wired thermostat-- is it possible to buy a unit that can be thermostatically controlled with a wireless controller?
A2: Yes, Carrier V, however I recommend against them if you wish them to control the furnace.. As Air Conditioners, or as Heat pumps, the only issue is the remote eats batteries like they were M&Ms but they work well... Just use a seperate t-stat for the furnace and they are great
NOTE: The Carrier V Units in my coach require 12vdc for control board ... If your unit does not have 12 volts at that hole in the roof.. Just ask and I'll tell you the so easy you may fall off the chair laughing work around.
Q3) I'm pretty mechanically inclined and have plenty of tools (mostly hammers and glue
) -- is there any reason that I shouldn't attempt this install myself?
A3: Well, it is suggested you have a partner assist you but .... Not really
Q4) Any other features/concerns I should be aware of while shopping for the unit?
A4: I think you have 'em covered.. You may wish to look at capacity of the unit and warranty and things like that, but I think you've covered most of what you need to cover