I saw on a lot of other peoples designs that they completely omitted C20. This capacitor is used to prevent oscillation according to the datasheet, but should not affect the output voltage.
I removed it and changed the 36.5k resistor with a 39k resistor. The regulator started giving me a reasonable voltage (~5.3V) that it MAINTAINED for a while, until about a minute later the voltage jumped up to ~12.5V and eventually fried the 100uF tantalum capacitor. I replaced the tantalum and dropped the 39k resistor back down to 36.5k but I am scared to turn it on again as I am worried that it will fry this tantalum (it is the last one i have).
Any suggestions are appreciated, this is rather frustrating.