I figured it out, kind of. I made a copy of the assembly and then methodically deleted components until the proper behavior was restored. I was able to determine that a single part was causing the issue and when I deleted it, it went back to normal. I then went through all of that components constraints and found that two of the "inserts" were specifically causing the problem even though they were not showing errors and appeared compliant.
When I examine the parts these were constrained to, I see how things could possible be slightly off in these two constraints based upon different mates (as the parts are related both directly and indirectly through constriants). It's just strange that the constraints were still built "correctly" and appeared to work but were actually having problems.
-Marked as Solution-