Having had a Mit HP ductless in my vacation home, I have a few comments to share. The unit has its drawbacks such as air noise, certainly less than a thru the wall or window unit but more than a piped in diffuser from a central system. I found it to be a bit annoying but grew used to it.

The other drawback was the constant air movement that some would perceive as a draft. With the air moving a properly sized unit should distribute the heat fairly well as the wall units discharge down and have an air sweep option.

No doubt the elect baseboard will be the quietist more and comfortable for heating; however it comes at a cost (energy use over a HP)

Another option if you are going to heat electrically is to consider electric radiant heat mats installed under the tile. This will keep the floors warm, at or below the cost of operating the baseboard but add 10X the comfort and would be supplemented with the fireplace.

For AC you could still go with a ductless or quality through the wall unit.

Here is a link that might be useful: one type of electric floor radiant

Electric radiant heat was actually one of our first considerations, especially before we thought there was a need for A/C. In talking with our architect and contractor, it was not considered cost effective which is why we next looked at electric baseboard. Now with our desire to keep some minor heating in the room when not in use, we are concerned about the energy efficiency of either electric method. There is no doubt radiant would feel wonderful to walk on which is why we first thought about it.

Regarding your mention of the air noise in your vacation home, do you think that was due to the size of the space you were heating with the Mit HP? Since the unit will only be heating one room for us, perhaps the air noise would be less than when the unit(s) are needed for a house?

I had a 18,000 BTU HP in a 450 sq ft florida room with lots of windows.

It would be like running a common bath 120 cfm fan is the best way for me to compare to for noise level.