Not sure about your transferring issue, USB drives over LANs can be a bit funky sometimes.
Looking at your log briefly, I don't see any signs of a crash?
But is looks like you are loading cue files (is this required? do you have one big file that has to be split via a cue?). It seems to me that you have set to auto analyze these files on import; Is this right? if there is a problem with the cue, or for some reason the audio analysis is hanging, that could cause problems or at the very least be really slow. and on top of it you have 3 USB drives .. thats a lot and could be linked to multiple usb connections over the same bus?? ;; (not sure just guessing)
If you have configured your autoimport to analyze the files ... uncheck that option. (at worst case it will make everything faster). Now restart JRiver and see if it crashes. Manually run audio analysis, making sure that there are no problem files which it can't analyze. (like a big wav or flac file indexed by a cue file). Recheck the option in your import config, after they are analyzed. Does it crash? (personally I don't think its really efficient to do analysis or auto cover art or whatever auto while importing even with fast computers and 6gbs internal drives, but that's just me ... you have 3 external usb drives with only 4gb of RAM (more than adequate for playback and control of audio of course), but if you are dealing with cue splits, analyzing audio and maybe more, could be a bit much.
If its not a problem with analysis, I'd look into the cue files.