I know the tool you are speaking of.. and I love that tool. 🙂 Best thing for a/c work. 🙂
These are special tools that allow you to change a shrader valve without having to depressurize the system. This is what my instructor used in my A/C class: http://www.ntxtools.com/network-tool-warehouse/MTC-58490.html
Here seems to be a cheaper version: http://www.ntxtools.com/network-tool-warehouse/MTC-81490.html
Now, back to your problem:
but my system only held the charge and stayed cool for a week.
So… you don’t need ‘special’ tools to remove the schrader valve since your system is no longer under pressure. So, you can use whatever you want to remove the schrader valve, like needle nose pliers or a tire valve stem remover for example.
Of course, pop the valve for a split second to ensure that there is no pressure (make sure you are wearing your safety glasses so you don’t freeze an eyeball) Or, use the environmentally safe method and hook up a manifold gauge set.
Now… all this work is under your assumption that the only leak in your entire a/c system is allegedly coming from your schrader valve.
Q: do you see green u/v dye around the taped schrader valve?
Q: do you see green u/v dye anywhere else on and around the a/c system?
Q: more specifically, can your system achieve -30hg” within 30 minutes, and hold that vacuum for 30 minutes with no more than 3lbs drop in pressure? if so, then your system is ready for some good old fashioned R134A.