Weird metal piece included with the new truetrac diff

When I bought my differential I got one of those as well. What you are supposed to do is bolt your rear axles into the rear end and see if you can slip the plug between the axle ends. It's purpose is to provide a means of checking axle clearance to prevent crushing the center section internals. If the fit is too high you are supposed to shave off the ends of you axles until they plug fits.

How exactly are you supposed to do that with an 8.75" rear end?

I too believe it is the thrust block that is only used on an 8.75" with the old adjustable bearings.