New to the forum, been lurking for some time.
I've run a 40 day Easy Strength program twice and loved it. I wish I would have known about it years ago, I'd be so much better off.
I asked for clarification of terms on Dan John's forum, which I'll summarize. Easy Strength from the book is 2-3x a week, higher load, low reps, basic human movements. The book goes on to describe "Even Easier Strength" and the original 40 day challenge which differs in being higher frequency, 4-5x a week, but lighter load. It seems that this second version is what most people mean when they refer to "Easy Strength."
DJ doesn't like squats for ES, others have found they can work. My experience is that I cannot squat and DL productively in the same workout. Whatever comes second suffers, they're just too similar. The first time I ran it, I did KB swings and goblets for a warmup, then leg raises for the "anterior," DL, incline DB bench, pull-ups, assorted loaded carries. That was the first time I worked on the DL, and I loved the program.
The second time I ran it, I was in a little suburban soccer mom gym with no real barbells, and no way to do proper squats, bench, or DL. So I did light front squats to try to get my wrists able to handle racking in front, and a suitcase DL. The front squat was really light, more like a goblet, so it didn't interfere, and the suitcase DL was weird. I didn't really like it, and probably won't do it again for a long time.
To the OP, my suggestion would be to pick either the squat or the DL to focus on first, run it for awhile, then switch. So, maybe do swings as a warmup for a squat routine, or goblets for a DL routine.
In sum, I loved the program. I always felt better after training than before, motivated to do it again.