A Raspberry Pi Zero and some UV LEDs are now on order. I will commence proof of concept tests with a syringe, LEDs, and some resin when they arrive. The motion tracking part will be developed separately as well as the pump. Currently waiting on the arrival of my 3D printer (Peachy) to construct the pump. The pump I've decided needs to be made out of two tracks of tubing with 3 rollers each, positioned 90 degrees out of phase so as to smooth out the natural pulsations one typically finds with peristaltic pumps. The body of this I plan to 3D print but if my printer takes too long to ship I will revert to machining it out of wood (to keep costs down). If pulsations are still too strong after this I will add a chamber with a permanently trapped air bubble of adjustable size and this will make it even smoother at the cost of adding a minuscule lag in changes to flow rate.
I suppose I should have done more research before starting this project but it appears that there already is a UV pen called the CreoPop. That said, I believe this project is still very justified as the CreoPop appears to have the same refilling problem that the Lix and 3Doodler have as well as a similar (slow) draw speed. I suspect that they are using LEDs whose peak wavelength doesn't quite match the peak curing wavelength. Additionally I plan to use more LEDs to cure faster. If the resin still doesn't cure fast enough at max power, there are very catalytic accelerators that can speed it up more. See a demonstration of CreoPop below.
Ideally I would like the maximal draw speed to be about how it appears in this time lapse at the 5 second mark. Because this is a time lapse, the T-REx curing speed needs to be about 4 times as fast. UV resins undergo exothermic reactions so speeding up this process means that I definitely cannot claim that my resin will be "cool." In fact it likely will be quite hot. Stay tuned for more updates.