How to enter an activity ID in the API Explorer?
To answer your different questions:


  I don't see what I would type in to locate it any other way?


You would locate it by typing in the activity subject. Admittedly, this isn't perfect because some activities might have no subject, and therefore can't be located via autocomplete.


  Is there a way to override those new GUI elements


Update: now the answer is yes :)
As of CiviCRM 4.6.9 an EntityRef in the Api Explorer will accept any integer.