I have a some what similar experience. The steel plate event I shoot doesn't allow any FMJ ammo as it flings large frags, which your range ought to clarify as the issue. There are coated/frangible rounds available that have a very light jacket to it, so light in fact that you can scratch through it easily with a knife. Or in other words a jacket so light that the round will still easily fragment into tiny bits just like lead rather than fling large frags. They are pricy, in my opinion - call me El Cheapo, but they should be allowed at your range or least show them what they are and offer to test them.
Also, JHP's should also be allowed as they do not frag as bad as FMJ's, or at least they are useable where I shoot, which is outdoors.
That said, I shoot the snot out of the Cabela's LRN's (lead round nose). I've put a few through my P2KSK and have not had any issue, maybe I shouldn't but then I did buy an HK and I expect to be able to do so if I darn well please. I mostly use my USP for these events and I've never had an issue with it. Thankfully these LRN’s are decent ammo at a decent price.
Last, there house their rules… Probably better off with a barrel that can shoot lead and won’t worry you.
Good luck with it!