If attendance is a problem for you, you wouldn't manage to clear the training phase, let alone work the actual job. Right now I'm on the second half of the training cycle, and my start time is switching practically every week - some weeks we start at 6am, others 8am. We even had one day of 7am the first week. And since they are running trainings days and nights, there are people who go from a 3pm start one week to an 8am for their ride-alongs.
It's a bit of a beast, and speaking as someone who always had trouble going to bed early and getting up on time... It's really been a challenge for me to manage it - but I was never disciplined on the job for attendance.
I wish I could say otherwise, but you really need to work on your ability to get to work on time *before* you try for an AT&T job.
As for HireRight - they contacted me directly when one of my former employers failed to call them back - I gave them the whole phone tree to call, and dug up my old direct deposit records from my bank (I no longer had pay stubs that many years back). They will definitely work with you if you are creative... If anything, I found that they were a bit overly reliant on, and trusting of me - made me wonder how many people get away with scamming the background check company, since AT&T places so much trust in them, and they don't seem to work that hard to get information from employers... Everyone I talked to had to dig up their own pay stubs or DD info if they had more than 1-2 previous jobs.