Hi dmauch,
You have a couple options here that I would recommend.
1. Depending on the type of passwords, they should be stored in your iCloud Keychain, which when you sign back into iCloud, iTunes, and the App Store, and other services on the new install will be automatically available.
2. I would (if you get Mojave to install) run it for a while before restoring backups to see how well it runs, and if it's stable. (if not restore to your High Sierra install.)
3. It may have been your time machine backup causing the issues with the Mojave install (if you tried to restore.)
Usually an in place upgrade doesn't require a time machine restore, (unless something gets broken.)
4. If in the event you get a successful install. Instead of running migration assistant, manually restore your backups from the time machine drive.
I have found in my own experience that this works the more reliable, and is the most dependable. While time machine is built into OS X, it's not the recommended solution for everyone for backups as it has a history and known issues of corrupting the backups. (especially over periods of long term use.)
I find to guarantee a clean experience, any applications should be installed and configured cleanly. Some apps are fine restoring the settings from backup, others it's just easier to start clean.
If you are going to try this, I would focus on the clean install, get Mojave running, use it for a couple hours. Then report back your findings. Then after that, decide on how to restore the backups.
These are the best solutions I can give anyone here to isolate all possible factors of something corrupt in the backup.
Those who have done the clean install, and still have been unsuccessful, there are other issues most likely going on with hardware preventing the os from installing.