My nice nearly cherry 97 XLT with side exhaust had an annoying rumble from 1500-1900 rpm. It was not related to any of the rotating assemblies since it was a single frequency. I surmised that the exhaust system was the culprit and that is what it turned out to be, but in a rather unusual form:

The side tail-pipe vibrates fore-and-aft like a tuning fork even with all the hangers normalized.

I corrected the trouble by adding a strut from the front leg of the tail-pipe hanger near the pipe forward to the frame. The connection of the strut to the hanger leg is through a silicon rubber damper. The rubber damper and strut prevents the pipe from vibrating fore-and-aft and the rumble is nearly tuned out.

 

Nice work!

 

As I read your repair, first thought was oh no, he has grounded out the pipe and other symptoms will pop up. Good going buddy, you have experience with this stuff. Too many people just brace it off and create all sort of NVH. (noise,vibration, harshness).

 

An alternative scheme which I have not tried is to triangulate the curve of the tailpipe with a solid bar between the hanger brackets at the rear of the muffler and the tailpipe. That arrangement would anchor the flexure of the pipe and move the resonant frequency well up-range. I might give it a try just for the heck-of-it and see if my deductions hold water....if it works, I'll post the results.

 

This mod to the first scheme eliminates completely the side-pipe vibration:
(Notice that the damper attachment point to the pipe is farther outboard.)