If your pot has a thick base (one of those with an aluminum plate encased in steel), that could be part of your problem. Try finding one with a thin base.
I have two 20 quart pots with thin based. Bought for $20 each some time ago and they heat up fine on my stove with up to 16 quarts in them. I'm not saying they are as fast as a turkey boiler, but seem to do OK.
I recently bought a new 22 quart pot. On sale for $35; thought it was a great deal. Nice and thick/sturdy, steel, with one of these even heating thick bases. Brewed a beer with it, 14 quarts in the pot, and had real problems getting it to a boil. In fact I don't think I ever got a decent boil. have been concerned about the beer, but seems to have turned out OK. Not going to be using that pot again for beer.