It's not a question of disk size. My hard drive is 1 TB, and the hosting company can hold unlimited data. There's no function for a thumb drive/USB stick at all. We're talking only about uploading and downloading from my hard drive to the hosting company servers.
No, the problem is, the file is so goddamnned big -- remember, it has 12 years of posts, more than 1.2 million of them -- that the server "times out" before the file is fully uploaded. And I learned how to tweak the server to enable uploading very large files, and I still had a glitch because of an "invalid character" somewhere in the database (Narrator: After 12 years, there are tons of "invalid characters" in the database, it's just how the world works).
So now I'm trying a third option, which is using phpMyAdmin to import the DB into a blank database. If that works, we'll move forward from there. I think I have the server tweaked correctly to upload the file, but phpMyAdmin is saying the max filesize is 2,047 MB and I think our DB is a little bigger than that. Like I said upthread, I'm probably going to have to submit a ticket to get it done correctly, and that means a few days delay, written tickets are assigned out in order etc.
Baby steps ...
Edit: If I can't do it alone, I can upload the file using FileZilla (SFTP) and then submit a ticket. The techs there will have better and faster computers, and they'll be able to install the DB. But that's only Step One Hundred And Whatever, because then the DB is totally configured for a different hosting company and will need to be re-configged.