Can you please just confirm that your use of "project" does not have
anything to do with project  Server and that you are using STS v 1.0 which
came out in 2001.

That is correct. This "project" has absolutely nothing to do with project  and
is entirely within the scope of SharePoint Team Services (ie, the old one),
to which we've applied SP3, by the way.

I wouldn't advise making amendments to the database  directly and given that
I can't think how to do what you want programmatically, I would personally
just bite the bullet and

a) print out the users  assigned to each different authentication part of the
site (thus getting name and permissions)
and
b) add the permissions  by hand

But then people have complained before that they want a programming solution
even if it takes longer in total (including investigating how to do it) ...

I was afraid that the manual approach would be the only viable
alternative.

Investigating how to do something (even when it takes longer than doing it
manually) often pays in the future, when you least expect it. Besides, I
maintain that there is no fun in administration, and if you can't think of
some way to make it interesting, you're probably not going to do it much
longer. And certainly not very well...

True in many cases. In this case with the application replaced over a year
ago, I wonder how many more times you are going to change domains  in its
lifetime.

There might of course be someone just waiting for their chance to tell you
how to do it. But recently there's only been myself and Roger who have been
even trying to answer STS questions here, so you might have a long wait.
(Thanks for the SP3 info - I haven't bothered moving my old sites to SP3,
they're still at SP2)