As much as I agree that you shouldn't fix what isn't broken, and if your horse is good and you're comfortable in those bits that's fine. But if you're not comfortable using those bits it's perfectly acceptable to change it!
There is NO reason your horse couldn't be ridden in any bit you want, it my take time for him to learn the new communication, it would take your time to work with him to get him to understand the change in communication. But if you want him in a different bit - he's your horse you CAN change it.
I personally, don't think any horse should 'require' a specific bit to be good. Some horses are better in specific bits, or more comfortable in others, but a horse should be good regardless of what you put in his mouth especially if your neck reining. I realize you're doing very finely tuned work, but as far as I know, with reining, the bit is the last tool of communication, seat, leg, body, and focal cues are all more important than bit cues.
So I repeat - there is NO reason you can't change that horse's bit if you want to.