In the thread you mention, the OP accidentally tried to run his process at a higher priority, which we obviously don't have the permission to do.
renice will alter the priority of already running processes. It works and has the quality that you don't have to enter a - or a -n before the priority you want to set the process to (unlike nice, where you oddly have to type nice -19 to set the priority to 19, you renice 19 a currently running process to set the priority to 19). You should also note that in this context, priority is synonymous with nice level and processes with lower numbers are "more important" than processes with higher numbers (trying to say this without using the word "priority").
Anyway, I don't think it's guaranteed that nice processes won't get killed and there could also be some memory limit that's operating here as well. I don't know any of this for sure so if you do think you know better, please speak up.
As you suggest, you can always untar this offline and upload the whole directory. If you use a good FTP or SFTP client, you should be able to do this in a straightforward manner with manually having to pick and choose files a few at a time.
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