i'm gonna take advantage of this opportunity, haven't had any debate in a while. his numbers aren't bad(if competition legit) but i still don't think they are high enough to only squat once a week. his numbers are pretty much what mine were competing at 165. i squatted once a week, deadlifted once a week, and did all my acc work. i just wasn't strong enough to make it work for me. now in the 198 class i have the highest official raw squat in the nation and it only took me 3 years. i squatted twice a week, hard, benched twice a week, and deadlifted every other week. it sucked, and i felt horrible all the time, but i think it was worth it. i just don't think he's strong enough to push himself hard enough to make squatting once a week work for him. plus like you said he may need to work on form, and only doing that once a week is hard to find your groove.
as far as training the low back, with some exercises this can be dangerous if you intentionally/directly work your low back. and i think working the upper back is even more important being that is the first part of your back that breaks during a squat or deadlift. i think exercises like front squatting work the low back and upper back in a safer way, and i highly recomend using a safety bar if one is a available. i did a couple sets of 225x20 front squats and had so much low back pump it was horrible.
i agree with trying to make every rep fast, that's something people should do more often, every rep, even warmup reps should be taken seriously. but i don't really agree with the pause squats, we did these in weightlifting for track but i've found much more benefit in various types of box squatting. i don't really like the idea of having someone pause squat because that's based on them staying tight like you said, people in general have a hard time with this. if you were personally there and could supervise it may be better but it's one of those things that people will more than likely completely mess up and cause more harm than good.
again it's one of those things that what works for some, may not work for others, but everyone we've trained has had great success with squatting multiple times a week.