I actually thought about suggesting this, too, but ultimately I don’t think it is a great idea for OP’s intended goals. Reason being that Dan John’s program really wants to you go hard on that lift (i.e. something like 7x5 heavy on your squat day) and I actually suspect OP would find recovery from the hard squat/deadlift days to be rather difficult.
I think OP would be best served with something like Daily Dose Deadlift.
If his max deadlift is currently 365, I would do this workout 4 days per week (say, Monday-Thursday):
…and on the fifth day (Friday), would do the same thing but have the last rep of the day be a little heavier (maybe 315 in week 1, 325 in week 2, 335 in week 3, etc). Run that for 6 weeks. Profit.
Of course, it depends if OP has more specific strength goals (i.e. if he wants to hit a certain number of pushups or pullups or something else specific). But if he is seeking general real-world strength, I think this might fit the bill. Certainly has worked for me.