The most effective location for standard ducted A/C would be the attic, since it provides a very short path for the A/C to the 2nd floor. This will be much more effective for cooling. However, it means you need to find a path to get the ducts down to the 1st floor. This may mean taking some space from closet corners or other areas so that you can run a couple of square vents down to the 1st floor, and then T out to run ducts left and right between the joists.

We were able to use a similar solution and the HVAC guy only removed 1st floor ceiling where the vents were exiting.

Bruce

The 9 ft ceilings might be your friend. Look at that level with an eye towards furring down in a way that makes it look like it belongs rather than having been added in. If you try to make it architecturally interesting rather than hiding it, you might make it work.

The AHU for minimally-ducted (low static pressure) mini split units are very compact and if you use two or three of them, you may find places to steal enough space for them inside the existing envelope. You might steal the upper reaches of a closet in one room and part of the adjoining room's closet upper reaches for ducting in that room and the next. You may lower the ceiling in an entry area and it can look good. Varying ceiling heights can be pleasing to the eye. I am going to assume that if you don't like the look of the most common, high wall mini splits, you won't like any kind of exposed ducting ;-)

There are also ceiling cassette mini splits and floor consoles. Have you seen them?

You can buy flush mount minisplit evaporators that look like a (large) regular registers (the mechanics are in the wall/ceiling void). However, I don't think that they are the best option for your particular house (lots of separate rooms). 7 foot ceilings are awfully low (the height of an average door plus trim), are you sure that's it? Have you had any contractors come out to confirm your suspicion that you can't run anything in the attic space (some of these guys are real small), or give you some other options?

If the home has been ok without cooling up to this point,you certainly won't need vents in every room. I live in N. Central Tx where we are experiencing 100F days in May. I have two central split systems with setback t-stats that alternate running 1 during day and 1 at night. If the hall door and a bedroom door at end of 18'hall are left open mid-day,the bedroom is comfortable. You need a combonation of good havc tech and finish carpenter working togeather. A small through the wall fan will solve some difficult situations for rooms where duct can't reach.