Hi Drew,
Briefcase LFBEXPORT_* logs are generated by the source repository's Laserfiche Server instance.
Briefcase LFBIMPORT_* logs are generated by the target repository's Laserfiche Server instance.
In a self-hosted system, those logs go under /pathTo/$Repo/LOGS/.
You didn't find anything when you looked in the source repo's LOGS folder because you have an import error, not an export error.
The "Laserfiche Server briefcase log: ****_***.log" (LFIMPORT_*) import log file was generated by the target, Laserfiche Cloud. I found evidence that Laserfiche Cloud stores these log files but it wasn't clear to me if or how they're accessible to end users (item #224415 for any employees curious). I'm asking around.
In the meantime, I believe that when you import a briefcase through the Laserfiche Cloud Web Client UI and there's an error, it'll show you the log right there in the UI. I'd try taking one of the briefcases that threw the error and importing it manually through the UI. That might be the fastest way to find out what the issue is in this particular instance.