Rules of thumb cause a lot of trouble in the HVAC world ...

10 BTU/sf perhaps? It might be even less. In which case, and this gets to the main question, even the smallest common mini splits at 1 ton / 12,000 BTU could be way over-capacity for any one single room, and therefore end up running in sub-optimal cycling patterns.

Inverters or units that have the ability to ramp up and down with 1% increase in loads (heat or cool). The problem is there are many incarnations of Inverters that don't allow a 1% step in capacity. So this is why you really need a trusted pro to do the work for you.

The other side of a true 1% inverter step up an down is you pay for over sizing (a bit) because and how the machine runs --- typically starts out slow and ramps up and down as needed you never over supply the space. The over supply the unit has is simply never used, because the algorithm the machine employs doesn't allow it to over supply the space in question.

Inverters add more complexity & cost: yes. Everything is moving that way so it's not avoidable for much longer. The con going forward will be how the inverter is designed to operate. 1% step up and down = better. ---- 2, 3, 5 speeds not so good for certain applications (climate is more prone to determine this in my opinion -- mild climates have much less trouble).

Assuming your existing HVAC system has adequate total heating and cooling capacity, a room with poor temperature control indicates an air distribution issue. Before adding the cost and complexity of additional equipment, I suggest you consult a HVAC design professional (not the typical service guy with a dog and a truck) and evaluate whether altering the duct work or installing balancing dampers will do the trick. I have a 1st floor master suite in my home and we use balancing dampers to keep the space comfortable. I adjust them twice a year--once for cooling season and once for heating season. The dampers are inexpensive and work great.

no one seems to talk about what the derated heat loading of the supplementary unit should be

It is not possible to discuss how much heat the supplementary unit needs to provide without knowing how much heat is being provided by the primary unit. Once that is known, then the heating and cooling loads for the room need to be calculated for your house and location. Once the heating load is known, then you can select the proper size equipment. In the case of a mini split, you have to determine from the manufacturers specification sheet what is the heat output at the outdoor design temperature you used in the load calculation.

There are mini splits available in the 9,000 BTU nominal size. If alerting the duct work to the room is not feasible, then you could close the supply vent and rely on the mini split for all heating and cooling.

If you go the mini-split heat pump route and attempt to use it to "supplement" the cooling provided by the existing system you're setting yourself up for poor temperature control. Cooling should be controlled by a single controller-- not two controllers which don't communicate with each other. Size the mini-split for the room's needs and isolate the existing system with a shut off damper.

Have you done everything possible to make the room more comfortable: insulation, caulking, shades, window film, etc.? Energy Star > Seal and Insulate.