Here are two pics I found on the internet - not mine. I couldn't find any pictures of the left side of mine with the stock muffler and my expired stock muffler went away years ago.
One picture is an original muffler and the other is a 1210 that still wears the stock muffler. What appear to be long nuts welded onto the muffler are where the stainless steel guard bolts on.
The stock muffler and short pipe that dump at the front of the tractor are shorter than my current setup, but the stock muffler is way heavier than the Cherry Bomb that's on mine now. So right or wrong, a quick seat of the pants (or SWAG) evaluation leads me to believe that the longer and lighter assembly could be nearly equal the shorter and heavier version when it comes to forces developed when the tractor wobbles.
If you do a search for a replacement muffler for a Ford 1210 nearly all of them look similar to Paul's and mine. They are noted as being for either horizontal or vertical mounting with no mention of reinforcing. That is another reason I don't feel there's much difference in vertical vs horizontal.
There isn't much of anything structural on the 1210 that would lend itself to being a part for added support.