On a natural gas unit I got from Dad (at 550 ft), he had the air valve/vane nearly all the way closed. I opened it as far as it would go and there was my sweet white/blue flame coming out of each burner hole. Then, I drilled the orifice out to about 0.015” or something god-awful enormous, and ooooh babeee. My big surprise was that I could actually run a larger orifice with propane that he was using with natural gas--I thought things generally went the other way around.
I concur, 30 lbs in less than 20 minutes is doable and you don't need a cajun cooker style burner. Many times those burners are hugely inefficient and just waste propane.
If you can get some closeup photos that might help. You may simply not be able to do much with it depending on the design.
WARNING: Your well-tuned burner may turn much of your pot support structure red hot before you know it. So, be aware that 20-30 lbs of molten lead in a pot jacked up on white-hot steel tubes or rods, etc., might just collapse. That can seldom have a happy outcome.