So far you've done great, Phineas! Thats an awesome increase, and it sounds like you've really got into the groove with your stance and form now.
Couple more things you can do to help, if you aren't already:
1a. As well as pulling the bar apart, when you get underneath the bar before you take the weight push the chest out and pin the scapula together tightly. I find it helps taking a very narrow hand placement so i literally don't have a choice, but my shoulder mobility is another thing i've worked on a lot. Keep this tightness all through the set. Your entire back should be solid as a brick wall all the way through.
1b. You can work on shoulder mobility doing dislocations -
How to Perform Shoulders Dislocations | StrongLifts.com
2a. Switch to low bar squats. Instead of having the bar on your traps, have it on your rear delts. Using that narrow hand placement and squeezing the scapula together, you'll make a shelf with your lower traps and delts to put the bar on. Wrist strength will be tested. This makes the weight closer to your centre of gravity.
2b. You may need to arch your back a bit more during your squat to accomodate this, because it might feel like the bar is going to slide off, haha. To take the pulling the bar apart technique a step further, you can help stability by trying to bend it around your back aswell.
3. Spread the floor. You might do this already, spreading the floor at the bottom of the rep is like leg drive in the bench - it really helps powering the weight up. Engages the hips and keeps the knees more stable too. Just try and spread the floor between your legs apart by pushing outwards with your feet.
4. Lately i've been tilting my head back to help keep my traps solid, i still look forward but my head is in a position where my eyes are pointing to the ceiling. Don't actually push your head back or you'll probably injure your neck, but it seems to help.
5. Squat a lot! Going heavy is great, but i've been doing a lot more volume the last month or two and it's helped no end. Do your heavys and get used to having a lot of weight on your back, but don't discount the value of sets of 10+ for not only drilling form, but building up endurance in the scapular stabilizers, traps, and supporting musculature in the back that you'll be using to keep solid.
Other than that, we've both come to similar conclusions about how to get the most out of squatting.