I have a core removal tool that occasionally allows me to replace the schrader without disturbing the charge. The reason I say occasionally is that I have encountered several systems (normally older) that will not allow the schrader to be removed once it has been unscrewed all the way to the top (and with 150 PSI behind it and the tool to catch it). I find with these problem ones, even later after recovering the charge and then trying by using as much pulling force as possible with a set of longnose, they still won't come out. I can only attribute this to maybe someone has screwed a flare style cap down so tight, it has compressed the end of the opening to where the value can't get past it.
How is one supposed to replace these cores that won't come out with a normal tool? I have just been giving up and putting them back, using a brass cap with o-ring.