Out of the above options I would prefer:
Using a remote line, macro line etc for the ASA fitting to release the regulator valve pin
Next - releasing the valve pin with an Allen key, screwdriver etc, but with care to prevent air blowing your hand (also wear gloves etc) and to prevent scratching or bending the pin etc
I don't like the idea of touching the burst disk (or even the fill nipple)
Bear in mind there are 2 burst disks - hp on the cylinder side, Lp on the ASA side. But remember its high pressure air even at the Lp end.
Mess up the burst disk and at best it's going to leak when attempting to fill, at worst the burst disk won't fail if over pressured
If you remove the regulator (after it's been drained) there remains the risk of damaging threads and it should realy be reassembled by someone 'competent'