Do you have any pictures you could post?
Pictures would be best with the saddle setting on your horse (not cinched) without a pad underneath. And then also include pictures where it is cinched up with your pad.
It sounds like your saddle is too big for him and the tree is too wide.
So I talked to a saddle maker who informed me that I can custom make a saddle to fit my horse to the tune of several thousand dollars...which he didn't recommend anyway since this was just a hobby. He advised that I just get a REALLY GOOD saddle pad. So off I search....
In general, this is HORRIBLE advice you were given.
Let's say that you play basketball once a week for fun. You actually wear a size 7 shoe, but you went out and bought a size 9 shoe. So, you wear 6 pairs of socks with your shoes in order to force them to fit because you don't want to go buy new shoes that actually fit.
That, in essence, is what you are doing to your horse. I'm sure you'd start to dread going to basketball once a week, because you are going to have to clunk around in shoes that don't fit. Your horse may start to resent gaming, if he always has to wear the ill-fitting saddle when he does it; even if it is only on rare occasion.
If a saddle fits very poorly, no pad is going to make up for it.
Does anyone have any advice on how to correct the fit of a barrel saddle on a gaited horse so that the saddle sits level?
Trial and error.
I've never owned a gaited horse but I'm assuming they are more of a narrow build. If so, you are probably going to want a more narrow gullet (although gullet size isn't everything; it depends on the shape of the tree too).
There are many websites that will allow you to send saddles back if they do not fit. Teskey's is one of them. Just read the return policy before you order. Some websites do have a restocking fee, but there are lots of them out there that don't. Teskey's Saddle Shop: Teskey's - Saddles - New Saddles