In such situation, it is always better to use the spare tire on one of the front axle and move that front tire to the back in place of the flat. The differential, even non lsd, will overheat because of the difference in overall tire diameter. Even my Corolla’s front diff whined like crazy with the spare tire on the front axle!Here is the message I received (while towing my boat with a spare tire installed)
I guess the message that you got was normal in your situation and shouldn’t trigger a fluid change.
That said, I did change my diff fluid early, I guess around 20k, and the fluid didn’t look good (looked like green paint mixed with silver paint). So I am glad I did it that early to get rid of break-in metals.
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