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Looking at some online pictures, the three phase electrical cables coming off the transmission look very very difficult to replace, if those are the ones you are talking about. I would suggest (after disconnecting all sources of power) a good cleaning of all terminals, a light coat of dielectric grease, proper re-torquing, and see how they do after that.
If your cables are getting corrosion between the actual wire and the end connector and that is the source of your issues, then yes replacement would be your best option.
I think your rear "muffler" is more like a resonator. Up to you on whether or not it would be worth removing to be able to add an aerodynamic diffuser in that location. I certainly wouldn't recommend aerodynamic treatment in this area unless that was removed. Putting sound deadening on the rear cargo floor and rear hatch might offset the sound that actually makes it into the cab.
Many people seem to find loud or obnoxious exhaust sounds desirable, so if it ends up too bad you can buy a sticker from your aftermarket exhaust company of choice. With this sticker attached to your rear hatch, people will believe you intended and spent significant money for the vehicle to sound like it does.
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