Best thing to remember would be to not get a live round stuck in the first place, check bore for obstructions before engaging ammo....
In the "range kit" is an old brass jag with the point removed for removing obstructions, stuck cases, bullets etc. Saves on damaging the internal thread of an expensive cleaning rod. Removing a live stuck round on a range is forbidden (go somewhere the RO can't see you and you can't kill someone else). Not too often someone is not able to fire their chambered round even if a ceasefire has been called but it does result in the odd case extracted spilling the powder everywhere and a slightly stuck bullet.
Glad the OP got it solved without incident, not the way I would have gone about it but I'm lucky that I can easily unscrew a barrel and attack things from behind. Handy things barrel vices and action wrenches / shifters. Also handy that shooting competition there is always a Gunsmith or two present for those nasty problems that need a solution.