half halts too much.. ??!!
Can't stop myself wading in here. Half Halts are too much, so you'd rather change bits. But then you say the place you ride is Centered Riding ? Isn't this all a bit back to front.
If you change bits to get better brakes, rather than working out what the root cause is, then you are opening yourself up to a never ending escalation of stronger bits.
Maybe your body language is not clear enough, so the horse does not realise you want to slow down. Maybe he's not listening and you need to work with half halts to get his attention. Maybe he's uncomfortable some how. I know my older (30 yr old) pony has to take his time slowing down these days. There are 101 possibilities for why he does not slow doan. ONE of those many could be that he is not happy with the bit you have. Have you given all the other possibilities equal time and thought ?
Half Halts should not be a lot of work, but it may need a bit of focus to fine tune your aids to your horse's training and reactions. (finding out where the buttons are). But then half halts should be like breathing - something that just happens without you even having to think about it.
Like learning to drive, you have to focus on it while you are learning and then it becomes more natural. Or walking - you learn to walk when you are a baby, but I bet you no longer have to think how to walk !
And if you have instructors teaching Centered Riding, then they should be able to help you use this approach to help with your issue.