I believe that Go to Related Records uses finds to perform it's magic. Could the scripts be running GTRR steps?
The finds might be happening alltimes the layout is displayed, but caching might be making all but the first almost instaneous.
Nope. We've isolated the issue to account permissions -- but we don't know why it's happening, or how to circumvent without giving fuller access.
If permissions include Record Level Access settings to make some records completely non-read to certain permissions users, this may be causing a behind-the-scenes internal search to determine which records can be displayed. If such permissions setting involve some interesting (complex or slow) calculations, those have to be evaluated for every record to determine whcih records can remain in the found set to display for the user.
Record Level Access is one of the all-time slowdowns in FileMaker's permissions system.
That makes sense. But the permissions are for a related table, not the table being displayed. So why would the find activate?
Another idea because the file is hosted:
As the file is opening, before any OnOpen script or Go to Layout on Opening, the layout where the file was last closed when used unhosted in single-user mode is actually be referenced even if you cannot see it. If that layout table involves Record Level Access, it may be forcing these evaluations before the opening script and layout triggers are able to be completed.
Try taking the file down from the server, open locally as a single user, go to a layout which does not reference any data from a Record Level Access controlled table (not even related calcs which look at such a table). Close the file on that safe layout, being sure that no closing script will change it, then rehost the file.