Okay, the Sony RAW files (ARW) worked fine, so it seems to be limited to the Nikon NEF files. Also, I'm pretty sure I tried pre-converting the Nikon NEF files to FITS RAW and that didn't change the behavior (but I'll check on that once more). I also need to reconfirm that this happens on my installation of PixInsight v1.7, but I really don't know whether an installation of v1.8 Ripley precludes going back to v1.7 (under Mac OS X can you have interactions between two, concurrent installations?). In any case, I have a "clean" install of Ripley on my Mac OS X 10.7.5 system and that shows exactly the same problem.
I also want to backtrack on one of my previous statements (that SOME work was getting done even after the integration enters this slowdown phase). It's possible that may happen under some trials for a short time, but it's just as likely that the system is entering a complete deadlock shortly after it reaches a small percentage of completion. So, it may not be a simple race condition, it could be a symptom of a memory or stack corruption where the process is just jumping somewhere it shouldn't be (and thus causing a deadlock rather than an outright crash).
Finally, after looking at some of the other "bug" reports on Ripley I'm beginning to wonder whether I'm just seeing a different symptom of a more common problem that is affecting other users and installations. In particular, it MAY be related to this report by user papaf: "Crash during master bias creation in BatchPreprocessing." Perhaps this is something that is being triggered by the way the code is being loaded (location) on each individual configuration. If so, and I can reproduce this under v1.7, then it may be a problem that was introduced in v1.7 (or earlier) and that has just sat dormant waiting for the correct set of conditions (that may now be more prevalent under Ripley). In order to confirm the latter, however, I need to know whether it is safe to have installations of both v1.7 and v1.8 on the same Mac OS X boot drive (stored in different locations and run at different times).