New 348 owner....Need some help

Can't identify your setup, but you seem to be missing the exhaust heat shields which that may help with your heat issue.
Is that round cross-bar aftermarket as well?

 

Ive not seen that set up before. The bumper should have some heat protection cloth on it but it may only be effective for radiated heat not a touching muffler. Looks as if it will be difficult to adjust forward which is what you need to do.
Heat protection.
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Oh I just noticed that the round bar is the exhaust support.
I think the cheapest way to get a gap is to shorten the end spool of the cat (they're aftermarket anyway), should give you enough to clear the bumper.
Otherwise, you can get new cat bypass pipes and exhaust setup from Superformance for relatively cheap.
Post pics of the new car!
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I was going to suggest shortening the cats as well, along with changing the mount bar attachment points (probably at the muffler attachment). But then it would effect the aesthetics of the exhaust tips exiting the bumper openings. If you add different tips... now its just project creep altogether. Best to replace the whole thing?

 

But at least you have plenty of room away from your tail lights. Replacements are very expensive and difficult to find.

Here's one of mine (since replaced):


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