By all means, go for it then. I'd still suggest 5 lbs per workout instead of 10 to try and get a little bit more longevity out of it, but the cool thing about 20 rep squats is your gains are just as much mental as they are physical.
I did 20 rep squats when I was at your age, weight, and strength level (and I'm still 5'10 too). IIRC, I started at about 185 and finished at 220 but that was like 10 years ago now. I didn't keep a log back then so I can't tell you for sure what my progression was like. The only advice I can give is to take the breathing aspect seriously. When the reps start getting hard, take as much time as you need and then get that big belly full of air before you hit another.
IMO, 6-8 weeks of that routine will be a great start to getting some baseline strength and getting past the mental aspect of pushing your body to the limit. In regards to the rest of your routine, I'd throw out the shrugs in favor of some light deadlifts (I'm pretty sure the super squats routine calls for RDL's) and mix up your M/W/F routine with some flat bench and overhead press as well. Maybe dips on monday, bench Wednesday, and overhead on Friday. You may want to even cut out the Wednesday workout.
Give it a go and re-evaluate in 6 weeks. If you're still making progress then stay with it, if not change to something else. If you are serious about this, then the best advice I can give is to remember it is a LONG journey. I think the super squats routine is a great beginner workout. If nothing else, it will develop 'toughness' better than anything out there. The bottom line is that you are at a point where anything is still going to work, so just keep working hard and playing around with it until you figure out what gives you gains and what you also just flat out enjoy doing!