So I wasn't able to find a solution. Instead, I simply deleted my laravel project, then recreated it as per the installation instructions on the lavavel site for the 5.1 documentation. I tweaked my config as necessary, then created a migration, then migrated, and it worked.
Finally, I transferred my files over to my remote server, and things are looking fine.
This isn't much of a solution, but I think I may have played around with the config so much that things just started going awry. Either way, my problem is solved by a fresh installation of laravel.
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