Switched to Creeper Host, at least for a while. Increased the server RAM to 5GB, and have the option of running multiple games from it now, including Factorio.
Updated the mod pack to v1.00.02 Alpha. For some reason, the old instances in the Curse launcher were not working properly. Probably because of the Forge update. Deleting and reinstalling a new instance of the pack using the Import file from the Curse project site seems to work just fine.
Let me know if there are any issues.