Kinda like this one?
Kohler KO-24 068 128-S Command Twin Muffler
View attachment 823528
Kind of like that, only if you moved the exit pipe so that it was facing the camera to the right of where the bracket attaches.
Somehow, in my initial perusal of the parts diagram, I missed the fact that the muffler itself does not include the exhaust pipe, there is a separate pipe and clamp, available from PartsTree for $35ish. But, I cannot find the Kohler part number for the muffler!
Here's the one I took off. I know the previous owner told me he'd replaced the muffler, and I'm guessing this is one that he had fabbed since the bracket is just welded on, as is the exhaust pipe:


Here's the relevant portions of the parts diagram from Simplicity:
Unfortunately, I can't find a Kohler parts manual that has the full list of Kohler part numbers - PartsTree, Jack's, etc all only list numbers for the parts that they still have available, which is very few. PartsTree has the exhaust pipe and clamp under the Simplicity part numbers, but while I can get to the right engine and spec and see the diagram from Kohler, nobody lists the muffler under a Kohler part number.
I believe the only part of this that is truly specific to Simplicity is the long exhaust pipe with the elbow at the end, and that is available... So is there another muffler that might fit the other parts?
Thanks!