Ideal component to switch 84V DC?
Use the MOSFET. Its use case is switching a DC load. If the LED strip has a lot of inductance, put a flyback diode across it. 

If you drive the gate with 5 V relative to source, then the RDS(on) is specced as 0.077 ohms from the linked data sheet. The power dissipated will thus be 0.27 * 0.27 * 0.077 = 0.006 W. No need for a heatsink.