The lie-in costs more than it gives
"If I get up early on Saturday I'll be wrecked all day"
You might be, the first Saturday. Let's look at why, and what to do about it, because this is the moment the habit reasserts itself.
If you've had five short nights, you get up on Saturday tired. That's the short week showing itself. The lie-in was hiding it, and now it isn't. The tiredness is real information and it's telling you the same thing the Van Dongen study told you in chapter 3, which is that six and a half hours isn't enough and you've been running a deficit that Saturday morning had been quietly disguising.
There are two things to do with a tired Saturday, and neither is to go back to bed at nine. The first is to hold the wake time and pay the debt from the other end, by going to bed early on Saturday night. An hour earlier than your weekday bedtime, on a night when nothing's required of you, is an hour of sleep that doesn't shift your clock at all, because the clock is set mainly by morning light and evening light, and an early night in the dark tells it nothing it didn't already know. Sleep at the front of the night is the same sleep as sleep at the end of the morning, without the drift. Chapter 18 is about this.
The second is a short nap, early in the afternoon, if you need one. I'll be careful here. Crowley and Carskadon tried a weekend schedule with teenagers that included an afternoon nap, and the clock still drifted, but their nap group also went to bed an hour and a half later than on weeknights, so the nap wasn't what moved the clock. The lesson is that a nap doesn't fix a late bedtime. It does take the edge off a tired Saturday. Keep it to twenty or thirty minutes, before three, so it doesn't eat into the night, and note that the NHS advises people with insomnia not to nap in the day at all.
Then look at the second Saturday. If you've held the wake time both days of the first weekend and gone to bed earlier on the Saturday, your clock hasn't moved, and Monday was better, and the week that followed started from a better place. The second Saturday you're less tired than the first, because the week wasn't fighting a drift. By the third or fourth the Saturday tiredness is mostly gone, not because you've got tougher but because the debt you were carrying has stopped being made worse every weekend. The wrecked Saturday is a one-off, or a two-off. The wrecked Monday was weekly.