Measuring very dim light-- charged glow in the dark paint
The tool I need should be able to be granular down to at least .01 millilumens, if that's even the right unit of measurement.

Lumens are how bright something looks to the eye, so unless everything you are measuring is exactly the same color, I would probably not use that unit.  Power or number of photons per second would be my first choice.

Are any current tools sensitive enough to get accurate readings from a 50-80mm sized source at about 3 feet? I'd like to take readings at several intervals like 5, 20, and 60 minutes.

I would use a camera or smartphone on a tripod.  The intensity values in RAW mode are proportional to the number of photons detected. Set your exposure time long enough to see however dim your object is, and be sure that your background is completely black. Note that JPEG is gamma corrected and so pixel value is not linear with intensity.