OVER CHARGE IT. Yep. I honestly don't Care what or how, other than being lucky and having a special built rig it's Not Possible to charge such a small about of gas. Over charge it, tape your temperature sensor to a place on the evaporator and start'er up. Adjust your charge to get a good temp on your evaporator and let it go. I've fought these small systems for years. I'll connect to the Low side and check the compressor, pull a good vacuum and hit it with the charge.
If you have a fast response sensor, you'll be able to see exactly what's going on as you "drop" some charge. Too much charge and the evaporator is going to be warm (40-50ish degrees, flooded) you'll be amazed how little you carefully remove to bring the evaporator temp down. On Marine refrigerators I normally go down to 10 degrees. They'll freeze beer in the bottom with the 'stat turned all the way down.
Yes, I know I Shouldn't But I Just Can't Help Myself...
Hook up your low side gauge to the process tube. Weight in the charge with electronic scale. Disconnect the evap fan and let the compressor pull the low side in a vacuum and sucking out the hose as well. Use a pitch off tool to pinch the process tube. Done.
If you consider that a standard 1/4" service hose will hold .33 oz/ft of liquid R134A, it would be rather simple to make a simple "dial-a-charge" device just using a hose. A 5 foot hose filled with liquid R134A would hold about 1.65 oz.