Jump in the queue a few minutes early on a phone and a computer browser (or two or three) and register yourself with the first one to get through (for the last several race weekends, positions in the queue are assigned randomly when registration opens to those in the early queue), then register your friend on the next one in line. If you wait and rejoin the queue after you registered yourself it will place you in the back of the line and result in less of a chance of getting the second registration.
If you do multiple browsers, make sure it is separate browsers (i.e. one chrome, one Firefox, and one Microsoft), not separate windows of the same browser (like two tabs in Firefox trying to get in will not give you multiple positions in the queue because the cookies the browser uses).
I had a 5k entry locked out while trying to register a second person for the Springtime Surprise and read about many other folks with similar experiences. So, unless your trip is contingent on both of you getting the race entries you want, I’d probably recommend taking care of your own first.