That should work pretty good. I'm not an engineer, know enough electronics, to have an idea of what going on. LEDs are low voltage device(3-5v). If the tape is rated for 12v, then there is some resistance in the tape already to drop the voltage. How close the tape resistance is to the incandescent bulbs will determine how well the Rheostat regulates the brightness. A one watt resister could added to compensate.
Larry
