Looking for Advice: Heat pump number of heads and location

[KVanier]

I didn't know too much about heat pumps when I was first looking into this so I assumed you should have one in each room that you wanted to control. After further research it seems that this is generally a bad idea and that most rooms in a home are too small to load a head by themselves and that you can end up with being a lot oversized and also it will be insanely expensive.

Due to this conception I got a number of quotes for a 7-head setup, as seen in the beautiful floorplan I have attached. This is like $40,000+ and includes 2 outdoor units of various suggested sizes (from a 2 and 2.5 ton to two 4 tons, which seems insane).
I'm trying to figure out a way to cut this down a bit. I was hoping to do something like an air handler in the attic that uses ducts to hit the 3 rooms upstairs but it's an unconditioned attic and that also seems like a bad idea. Will 1 head on each floor (of correct size) manage to cool and heat the entire floor if doors are kept open? Maybe 2? Kind of want to be able to close the main bedroom and guest bedroom doors though.
There's no ducts in the house of course and heating is all electric baseboard. The only AC is a wall unit where the #4 position is and it's not particularly effective.
I had an energy assessment done and am just waiting for the results which should give me a design heating load so this is probably more about positioning and how well the air will exchange between doorways.