I think I found something a bit more suitable than the 2N2222A.
http://www.mouser.com/ds/2/149/BSV52-888642.pdf
This part is more suitable for this application. According to
this calculator it should require a 350k resistor on the base assuming a 50k load on the collector. Closest standard resistor is 330k, the calculator triples the current to ensure saturation so this should be fine.