Deadlift Max Follow-up

A couple of weeks ago on Max Effort day at the gym, I deadlifted 110 kilos but failed on 120. Someone asked about quarter-deadlifts as a way of increasing your lift. Dave told us you can do that by putting the weight on a low rack. That way you can lift it off the rack and get accustomed to the heavier load, even if you can’t yet pick it up off the ground. I guess the legs are stronger at that point of extension.
So last night Nancy and I tried that, and I lifted 120 kilos (twice my body weight) off of the rack three times. The first time, I tried to set it right back down into the hooks after I stood up with it, and I missed on one end, which crashed to the ground. We picked them up. On my second lift, I stepped back and dropped the weight intentionally. It was hard to step back while holding the weight. On my third lift, I set the weight back down into the hooks.
We did this after the main workout, which was an unusually mild strength workout that included L-sits, front squats, military press, and two or three max sets of chin-ups (palms in). On the front squats, I worked up to 60 kilos, not a new max but kind of heavy. On the military press, I only managed 35 kilos. Max sets of chin-ups were 7 and 5. Out of all that, what I feel today is the distinct memory of the 120-kilo deadlift in my legs and rear.
I hope I can remember to do those partial deadlifts every so often until I can lift it off of the floor. Nick told us to create pressure in the abs when starting a deadlift, as hard as we can, and focus on that exclusively. Dave says to focus on crushing the bar in your grip.