Planning central AC/Heat in 250 year old home

Hey guys! So I'm apparently signing a purchase contract for a home built in 1778 today, because apparently I have too much free time and not enough stress in my life as a small biz owner. It currently doesn't have central air, and the heating is handled via individual radiators in each room (centrally controlled, though).

Upgrading the system is not a huge priority, given that I'm in the Northeast and we're fortunately past AC season, and I think I can live with radiators for a winter. That said, I'd like to get a system put in hopefully by next summer, and had some questions just for my own rough budgeting.

It's a three floor home, though only two floors are finished and real floors. There is a large uninsulated attic and basement. Both are, as far as I can tell, outside of the thermal envelope of the home (insulation between floors). So there's room to add ducting and compressor/blower units. There is no room in the walls to run ducting between floors, though, without significant work and $$$ (it's all plaster on top of 300-year-old wood.) I would prefer not to build out soffits to add ducting in the living area because the ceilings are already relatively low and the rooms are not huge -- turns out people were very small during the American Revolution. I would also prefer not to run anything along the outside, as the original look of the home is one of the main things that drew us to it.

So my questions:

1. Is it possible to split the heating an cooling, have the boiler in the basement with ducts blowing up, the AC in the attic with ducts blowing down, and then just put in some active vents between the two main floors with reversible fans that blow cold air down and hot air up, or just circulate all of the air? Is this a feasible approach as a potential solution?

2. Does it matter if the boiler is in on the bottom and the AC is on top, or should they be co-located? I assume there's efficiencies gained from having the air mover in one place for both systems, but doubling that cost isn't a deal-breaker given what the total renovation budget is likely to end up as.

3. Would it make more sense, from a comfort perspective or feasibility perspective, to just install two individual (but connected for control) systems? So like a heat pump for heating and cooling in the attic, and a separate one in the basement? I assume I'd be able to size both units down vs. one unit for the whole house.

4. Does it even make sense to convert the radiators to forced air? I honestly don't know what the advantages and disadvantages are.

I know that's a lot, and really appreciate any insight y'all can provide. Not looking for any final answers, since I know that's way beyond scope, but just some hints at what direction to start thinking in.