Sounds like he needs training, not more bit.
Not sure what you are referring to by a basic western shank bit, that tells us nothing about the mouthpiece and shank shape and length.
Unfortunately, when a rider is having an issue with a horse in a particular bit, they tend to think they need to switch bits instead of switching training methods.
The only variation in bits you should be worried about at this point with a green horse is what mouthpiece he prefers. Single break, double break, lozenge or French link and loose ring, fixed d or eggbutt or full cheek.
Make your thoughts, your horses thoughts. That means not getting into a tug of war. That means going as slow as needed. In my opinion, if he’s dragging you around in a snaffle, the horse has no business loping until that’s addressed.
Long lining could be beneficial, also the help from a qualified trainer or coach. It’s much harder to untrain a horse that wants to fight pressure than it is to teach them to give to pressure from the start, don’t dig your hole any deeper.