Thanks Colin!
I had created a Developer Topic to see what options others recommended for this, and to document my own testing. It can be found here:
The best currently available approach/workaround, at least for the email, seems to be using the “exact” keyword, which allows you to search as one would expect, and does not return ALL identities when using the actual full email address. This might be good to have documented on the Search page. However, it fails because it is Case Sensitive, so if you do not know the case, then the approach Colin mentions quoting the whole thing, is correct.