Like Zach told, probably your diff is melting cause it slips...
The track I'm driving at has a straight which has a length comparable to yours.
What diff grease are you using, I found there's a lot of difference between them. I strictly use the red associated silicon diff grease (not the stealth diff grease).
When using ceramic balls (dont know for carbide), I do the following to prep the diff:
I glue the diff plates to the outputs with ca glue, I put a extremely heavy polish compound on the balls/ plates (no grease, Paint cutter), after this put the diff together and tighten slightly, when its running light I start playing with it.
This makes an awfull sound, you are now letting the CERAMIC balls cutting a groove in the plates, I regularly add some more polishing compound and keep this up untill I have a good, kinda deep groove.
When this is done, completely clean the diff very thoroughly, all the polishing compound must be gone.
Now lube the diff balls with the asso silicon diff lube and tighten till it doesnt slip.
Why, ceramic balls are extremely hard (they dont get damaged by this, not even the slightest) so the contact with the plates is minimal, by making a groove there's more surface of the balls touching the plates. More contact -> more grip with less pressure -> extremely light running.
More info: http://www.markpayneblog.blogspot.com/
This works really well with ceramic balls!! Maintenace, just clean the balls and plates + relube, done
I never had a melted diff and its allways in perfect working order (driving 1/12th learns how to do a diff....)