Many projectiles used at ranges are soft lead. .22 rounds, commercial swaged lead bullets and the cores of most jacketed bullets. They only really hard lead projectiles you are going to likely encounter in the average range lead are cast bullets which are solely a reloading proposition, and on most ranges, going to be in the minority. Those cast bullets are likely going to be easy to sort out when intact, and they tend to stay intact better than the softer ones. If you know someone that casts bullets for cartridge guns you could trade the hard stuff to them for some softer lead.
I'd give it a try. I am sure it will work. Just work out a load, and as you said patch thickness, and you should be good to go.