Google is great at providing 20/20 hindsight. 

The little problem I was having with insert triggers is (unsurprisingly) not uncommon.  I googled a bit after a suggestion in a comment (thanks El Guapo) and found a great explanation by Mike Taulty on how to deal with just such a concurrency problem.  He’s specifically dealing with a timestamp column, but the issue is essentially the same. 

Good to know…