Thanks trailhorserider! I had meant to get back to this to thank you but time got away from me.
Anyway, in good news, I was looking in that sidepull idea and I discovered that my lil "Indian Bosal" shindig could be taken apart and, with the addition of a curb chain, turned into a sidepull! Fancy that!
I bought a curb chain today and sadly it was HUGE on Lacey (and it was the smallest one they had in the store! I didn't think her muzzle was that tiny...), but I made it work. Then I rode her in it to see if she approved and she totally did! She was almost softer in it that she is when it's a cross-under! I even tried turning a few times like the kids always want to and even though she gave me dirty looks (if looks could kill...oh man) she understood what I was asking and turned promptly.
We'll have to see how she does tomorrow since we have two lessons tomorrow, but hopefully she'll do well for them too.
So thanks for that idea! Hopefully it'll be "the right" one!