Looks like a lot of hardware for one horse's mouth, if you ask me. :/ I moved my horse from a snaffle up to a junior cowhorse, only because I plan on showing him as a reiner in the future and he's too old for a snaffle to be legal to use on him in the show ring.
I WILL say that a myler bit like that (without the nose band) would probably be a good transition bit, but I don't know you or your horse so I can't say for sure. I'm no expert, but that sounds like a logical progression from a snaffle. Good luck!