Is it possible to re-install from scratch?

Since there’s been no help on the upgrade issues from 7.6.4 to 7.7, and I have no access to account details (see, I am wondering if I can just install the website data fresh and run the repair tool from the admin panel?

When you say install from scratch, do you want to keep existing data?

You should just be able to unzip the download zip/files and run a fresh install on your web server without issue.

If you wish, you could then point this instance at your 7.6 db and run a quick repair & rebuild so it adds any new definitions/tables/fields for the 7.7 release.