Some good advice here.
I booked a UA ZED fare earlier on this year and in the end had to buy a revenue ticket for both sectors as I wasn't going to get on both of the flights. On my first sector, I was number 14 out of 14 staff trying to get on a 737-800 with 11 spare seats available and everyone else was UA staff!
For me personally, the seats 'taken' on the seat plan didn't accurately reflect the loads on the day so be careful in how you use that.
I know we are not really supposed to call reservations with load enquiries but I resorted to calling UA reservations for the return sector but explained that in addition to the request for the loads, I had a genuine desire to purchase a revenue ticket if the loads were looking busy. That worked for me and after being told I had a pretty slim chance, I just sorted out a ticket over the phone and it was sound advice as even some UA staff were bumped off the return sector.
I had some issues with the airport staff insisting it was a paper ticket on my first sector but after politely but firmly assuring them that EK no longer issues ANY paper tickets, they made a few calls to UA and were more the wiser for doing so. Leave yourself plenty of time.
Good luck with the loads!