Muffelr replacement on B&S Mdl 40577-0317

I inherited a Cub Cadet ZRT50 mower (I think it's a 2004 model) , and the output from the exhaust is burning the grass. The muffler has a deflection plate that is angled slightly (30 deg?) towards the ground from horizontal. I have rotated that plate so that it sends the gases out horizontally -- any reason not to do that? Also: is that defelction plate really required? Couldn't I just leave it off entirely?
(As a warning to others who may be tempted to do the same thing, in removing the plate, I managed to snap two of the little screws that hold it on the muffler. I just used some old sheet metal screws to refasten the plate in its new position.)
In researching the Web, I see that many others have experienced the problem of burned grass whenever the mower is paused for a minute or two. I got to wondering if someone may have devised a replacement muffler, or muffler shield, that cures the problem. But in searching for replacement mufflers, I'm having a hard time locating the correct part for the one that's currently on the mower. I can find parts lists that show part 696226 for model 407577, but with a different type. Whenever I search using type 0317, I can locate a parts list, but the seller never seems to have the muffler for sale. For instance, I can find that 696226 is used on 40577-0112, etc. but not whether that muffler will work on 407577-0317. So that's my next question: will it?
And lastly, when I do see pictures of muffler 696266, it doesn't look at all like the muffler that I currently have. The one that's on my mower has a bunch of perforations (which are covered by the deflection plate) where the gases exit - as best I can tell from the pictures, 696226 looks like it just has a little pipe nipple where the gases leave the muffler. Am I interpreting the parts lists correctly?
Thanks for your help!
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Sorry - all references to "40577" should be to "407577."

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