Is it possible/efficient to have One mini split unit in the living room and remove all the ducts in that room to then have the central AC only cool bedrooms?
However it might also be efficient to let the mini-split be active and use fan/blower to circulate air throughout the house. One example of this is for dehumidification. On the old "bang-bang" A/C systems, the units have to run for a long time for dehumidification to be effective. Well if it's deep clouds (no solar gain) and 75F outside, the big system will run 2 minutes an hour, which won't dehumidify a thing. However, if you run "blower only" to circulate air, and have only that mini-split running, it's going to run continuous at low speed, doing A/C for the whole house. That means it will do a good job removing water.
So I would just make sure your return ducting is tip-top (so it works properly) and try that.