It sounds to me like he was a properly trained western horse (if by neck reining like a beast means he's good at it
) and he wants less contact with the reins, not more. A western riding horse should
go on a loose rein, with only the weight of the reins to turn him.
What also supports this is the fact that he likes the split reins better than the barrel reins. The only reason the horse would even know the difference is if the barrel reins were too short for his liking. (When I bought my Mustang he was a roping horse and the guy rode him in the shortest reins I ever tried! I couldn't stand them and the horse couldn't relax and put his head down if he wanted to. I do
ride in roping/contest reins, but I only buy ones that are a full 8 feet long, preferably a few inches longer).
Honestly, in my personal opinion, he sounds like he needs some relaxing, calm rides to just get to know you and get back in the swing of being a calm, confident riding horse. He doesn't sound like he is ready for the excitement of barrel racing, and if that is truly his personality and he doesn't calm down over time, he may never be a barrel prospect.
I wouldn't go to something more severe for him bit-wise. If he goes well in a snaffle on a loose rein, then give him a loose rein. I would get him to be a calm and confident riding horse with as mild a bit and as loose a rein as possible before I tried to get any kind of "performance" out of him.
Just have fun with him and trail ride him (if possible) and don't think about barrel racing until he has his "issues" worked out.