You can't opt out of the 80 hour work week, and no waiver is going to save a program. What you do see happening sometimes is that programs have residents fill out time cards and if the numbers come back too high, the less scrupulous programs browbeat the residents into resubmitting time cards that are within compliance, regardless of whether true. Honestly, at most programs the 80 hour duty hour restriction is abided to with most residents working closer to a 75 hour work week, thanks to inventions like night float.
As for the initial question about regular sleep patterns as a resident, you can forget it. There are LOTS of variations on the theme, but none give the typical intern a 7 hour/night regular sleep schedule. You either see q3-q5 type calls (see the q4 schedule that group_therapy posted above, which is pretty typical, with 30 hour long call), or you have night float. The way night float tends to work is that you come in at 6pm and leave at 7am for 6 nights in a row, with your day off usually falling on a weekend. The downside is that since you are leaving at 7am on your "day off" you are actually in the hospital for some time every single day. The up-side is that if everyone in the program does a month of night float, you don't have to have nearly as much overnight call the rest of the year. But in that month you basically have to sleep during the daytime, because if a program is only having you work a 13 hour shift/day, they aren't going to expect you to be sleeping during it. It's the transfers from day work to night float and back at either end of the rotation that tend to be hardest on sleep patterns. It's very hard to go from sleeping days to sleeping nights, and you don't usually get a weekend off to regroup and get back to a normal pattern.
Finally you guys should realize that during 30 hour overnight shifts you may get some sleep a few hours, but not infrequently will be spending the entire call working and not sleep at all. I can count on one hand the number of nights I actually saw the call room, and even on those times you will inevitably be awoken every half hour with various foolish questions that didn't really need to be addressed at 3am.
So in short, no you won't get regular sleep as a resident. you will learn to sleep when you have the opportunity. Like whenever you sit behind the wheel.😱