I figured it out.  I set up a memory variable that I would just accumulate all the SegCount amounts until the SE was ready to get outputted.  When it was time to output the SE, I'd take the memory variable + 1 and it would get the correct segment count, then I'd clear the variable.

Thanks again for your help, Kimberly!

Thank so much, Kimberly!  Looks like that is one (very important) piece of the puzzle.  I have the ST/SE's outputting every 10 records but it looks like the SegCount only counts one record at a time.  For instance, there are  156 segments, including the ST & SE, and the SE count was 13.  I'm going to have to dig into those EnsLib.EDI.X12.Document  properties and see if anything there can help me.  Really appreciate the nudge in the right direction!