Really interesting form of progression, after I run out of LP I think I will be swapping to a 1 lift per day template so I can spend some time focusing on cardio afterwards. Was thinking 5/3/1 progression initially (with a light 3-5x5 backoff after main work set) but will keep an eye on how you progress here.
Have the DOMs reduced at all with time? Are you only experiencing them for Squats or all lifts?