Plasterboard Work
It is often possible to run a new cable between a fixture and a switch without tearing up large sections of drywall.
If you can visualize the wire going up the wall from the switch and then from the corner of the wall/ceiling to the fixture, you may be able to snake a new wire.
Cut a small hole in the ceiling in in the plasterboard immediately above the switch.
The issue will be whether the hole in the ceiling allows you a straight run to the fixture box (along or between a ceiling rafters). If not, you nay need to cut more small holes where the cable would have to cross a joist/rafter.
If it is a clear run, you may be able to run a cable from the ceiling hole to the fixture box. Then you can cut a small hole in the wall immediately below the first hole.
You also need to be able to drill through or notch the framing (without seriously compromising a load bearing wall) to allow a cable to pass through. If this is feasible, you can drop a cable down to the switch box, thread the other end through the hole or notch in the framing, and extend it to the fixture box. If you are notching or if you are drilling at less than 1.5 inches in, you need to put a special metal plate over that spot to protect the cable.
Later you can patch the small cutouts, tape over and paint.
Wiring
You can continue to use the existing cable to power one circuit and use a 14-2 cable to provide the hot leads for the other two circuits (they will all use the neutral already on the circuit. Since both wires in the new cable will be hot leads for a circuit, the white wire needs to be marked at the switch and fixture to show that it is hot.
You can find three switch units that fit a single gang box, or expand the switch box to double gang.
If you want to use a wall fan control, you'll likely have to remove the remote fan control receiver from the unit. The remote receiver in the fan housing controls the fan speed, and will not allow the wall control to override it.
In the most basic case, the remote receiver will have "input" wires connected to the standard household wiring (ungrounded, grounded, grounding). The unit will then have "output" wires that connect to the fan, and/or light kit. Because of this, controlling the "input" of the remote receiver will have no effect on the "output".
The procedure for removing the remote receiver will completely depend on the unit.
Best Answer
In your case you are fine. The switched receptacle covers NEC Article 210.70(1). If you feel you would still want a switch at the entrance you can always install a wireless control device.
Reference: https://www.homedepot.com/p/Universal-Wall-Mount-Ceiling-Fan-Control-99111/203690000
Good luck