Started prototyping the joule thief circuit to see if I needed to tweak the components a little.
I wound the toroid with x2 24" 28 awg lengths of magnet wire which ended up with ~23 Turns.
I then set up a basic run of the mill joule thief circuit.
Through testing I found that a 20k potentiometer worked better for providing a good dimmer control vs 5k. I placed the pot between one of the outputs of the toroid and the transistor base.
Manually charging the supercap with a battery to 3v allowed me to test the run time and voltage.
I was able to run a full 1m length of 5v cob led string for ~2-3 min from 3v all the way down to ~ .4v.