Just a thought, maybe it's not the reel, but the way you're spooling your line onto the reel. If it's twisted at the beginning, the whole spool is going to be twisted no matter what. When you first spool line on, after 10 turns of the handle, stop and take a look at you're line. If it starts to double over on itself, flip the spool of line over and turn the handle a couple more times, stop, look, and repeat until you don't see it twisting on itself.
Or possibly, it could be the lure you are throwing. Such as, in-line spinners (rooster tails) will greatly increase your chances of line twists because of the way they spin. That's if you tie directly to the line without a swivel.
And if you still believe it's the reel, you should definitely look for a reel that has a bearing supported line roller. That should help with less line twists.