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I have had good results using Another of "removing the check valve" . 1st remove the brass valve as explained then - I have a small drill press (or a hammer and punch could be used. I put a #40 drill bit (or a 3/32 bit can be used) in the drill press Backwards (with the cutting end pointing up) and simply bring down the bit to the bottle and push the check valve down into the bottle and leave it there. Then remove the bit, tighten the chuck all the way and use the bottom of the closed chuck to re-install the brass fill valve. So far all the ones I've refilled (15) have worked fine.
I started to use the sheet metal screw method first and thought since I was modifying 15 bottles that the press would speed things up - it did.