You added 2 cans, but how much was in it to start?
Most of the cans we deal with are 12 oz cans. 2 of them = 24 oz. If as it was said, the capacity is 1.25 lbs (20 oz,) just the 2 cans puts you overfull staring from 0. Add that to whatever was in it - and you are way overfull.
Q's - it was cycling before you added it? Were the tubes near the drier cold or very cool before you added?
If there is a restriction somewhere - like in the expansion valve, it will cycle because the pressure goes too high, the hi/lo switch shuts it off. If there is a restriction flushing may help, or replacing affected parts.
When you don't know how much is still in it but don't have the equipment to suck it out and store it, best way is use a thermometer (meat thermometer from the supermarket does fine) in the inside vent, windows closed, AC on high recirculating.
Add the freon slowly while watching the temp. Keep adding till the temp stops dropping and starts to go back up. Stop, finished! You are looking for maximum cold.