I've 'lost weight' (I'd like to think mostly fat, but probably not) running 531 and I agree with most of what you say, except maybe #5
Something I've picked up on this site, is that fat loss is 'easier' with lower volume. The idea being that additional volume generally means that you're doing more work and this will be hungry. Since fat loss is mostly diet, cut the volume and you can consume less calories and not feel hungry all the time.
With 531 I did this by using a low TM (80-85%) and starting a new 5/3 cycle (weights are lighter). Hit your main lifts and maybe a couple FSL sets. The goal is to maintain strength. Now you can focus more on conditioning.
I liked doing the 2/2/2 program.
- Lifted 2 days a week (SQ/Bench;DL/OHP - 531 (5pro) then maybe 3x5 FSL with some lat and abs as supplemental)
- 2 days of conditioning. battle ropes, BB complexes, sprints, walking with heavy shit, etc).
- 2 days mobility
- lots of (vest) walking throughout the week.
But yeah, diet is going to be super-important here.