Is this a high pitched hum?
After I installed my ARB locker in my rear m226, I had a soft high pitched hum around 45 mph, and it was when I was pressing on the throttle. It turned out we had not set the bearing preload enough, once we cranked it a bit further the hum disappeared, and has not come back in the 2 years since. I've also heard if the pinion preload is not set correctly you'll get the hum as well.
Did you start hearing the hum after you switched tires? So maybe it had been there all the time since the rear diff work but was masked by the mud tires?
*edit* nevermind, didn't read far enough int the thread, sounds like you found the issue.
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