I'm currently putting in my 3rd system. So far there has been an LG wall mount unit, LG central unit, and Fujitsu short ducted unit. In the first two, I did the all the electrical, installed the physical units, and ran the refrigeration lines. Then an HVAC tech ($300) did the final connections of the copper lines and vacuumed them. This time, I bought the equipment needed for the vacuuming. Since the price for a professional is more than 2x DIY, I can't be bothered with the extra warranty coverage for that price difference. I'm not sure what Mr Cool's warranty is since its geared toward DIY installs.
I don't have any experience with Mr Cool, but they do make central ducted units
https://mrcool.com/central-ducted/ so it is a possibility if you want to DIY and use your ducts. There are losses associated with ductwork-- heat/cold and heavier duty blower. If you don't want to reuse your ducts, you could potentially install a wall mount unit at the open end and condition the entire house. I think that would largely depend on how well insulated your house currently is, how many bedroom doors stay closed, and the wall configuration. I don't know if Mr Cool has them, but there are also ceiling mounted short duct units that can go in a closet, which would then blow into adjacent rooms. Could you upload a sketch of the layout?
I have been told ducts usually need to be redone because newer blowers operate with less pressure (head) but I haven't looked into it. I tend to think thats just HVAC companies wanting to pocket more money. If your old ducts were designed for a single stage blower and gas furnace that comes on at full blast for 10 minutes at a time, it seems logical that an inverter driven heat pump blowing 100% of the time at much lower cfm should be perfectly fine.
I'm curious of the implication of the Inflation Reduction Act. If you buy the unit now, would it be eligible, regardless of your personal income situation? I haven't seen anything clearly written about it. From what I gathered, it won't be implemented until 2023.