(Incomplete answer containing only references.)
Is there a way to get Mathematica to export chunks at a time and stitch them together afterward, so as not to hit a memory limit?
Yes, I already publishedpublished (see "EDIT 4" section) such a technique on this site. Another method is suggested by Vitaliy Kaurov (search for "3dImagePartitionExport.nb" in this Wolfram Community thread).