If the angle of the bars or the gullet is indeed too narrow for your horse, NO, there is nothing you can do with padding.
Just like there would be no way you can make a pair of shoes fit your feet if they were too small, by altering your socks.
However, is the saddle truly “too narrow” or is it actually too wide and therefore “dumping” on the shoulders? (It will make it look like it’s tight on the shoulders.)
I went through saddle fitting with my 6-yr-old this past year. Just about every saddle either “dumped” on his front end or had too much rock in the tree (and the back came up). Here is an example of a saddle that is TOO WIDE and thus creating a tight spot on the shoulder. I even tried the exact same saddle in the more narrow tree and there was still a tight spot on the shoulder. Tried at least 10 saddles until I found this one that fits like a glove. And it’s full quarter horse bars.
Are you able to post pictures of your horse and any saddles you’ve tried? Again, just want to make sure they are indeed too narrow … and not actually too wide and dumping on the shoulders, creating a tight spot.
I have a similar-shaped horse, by your description. For him, the Circle Y Flex2 WIDE saddle fits him absolutely perfect. I barrel race, so I have the Lisa Lockhart version but I know that saddle is available in other disciplines (including trail). So, maybe something to try.
I’ve never heard of anyone searching by the swell for saddle fit. Usually that’s more for the riders sake and not anything to do with the fit for the horse.
Here’s one website and also another that have great info on saddle fit.
Yeah, saddle searching stinks. Your best bet is to find a tack shop that you can haul your horse to, and try saddles on. If you have nothing in your area (like me!!) then you are stuck with ordering saddles online. You just won’t know if they fit until you try them on.