Agreed on the frequency. Multiple sessions, training the right pattern a few times a week may be better than just doing 10 x10 in the deadlift on 1 day.
You could try Romanian deadlifts to learn to use your hams and glutes more. If you add bands to the bar, it gets more difficult to lock out at the top of an RDL. This really taught me to finish by pushing my glutes through instead of extending my back. The extra "weight" added by the bands makes you get the hips in and under. I got this from the power lifter Chris Duffin. He's got a lot to say about glute activation, abdominal pressure and proper hip position if you're interested.
My favorite lifts for upper back strength are bent rows and shrugs, but when I had my own over-extension problem it was difficult for me to set up for these exercises. I would always arch too hard over extend, and end up using my middle back/erectors to kinda heave the weight and take the stress of my upper back. Chest supported rows and seated rows on the cable helped. Really let the weight stretch you at the bottom, then use the upper back, not the lower and middle back to start the pull.
I'm not sure what first caused my to start to over extend my back, but when I started trying to fix it I leaned my obliques were really weak compared to my back and "front abs." I tried sidebends and stuff, but 1 Arm Farmer's Walks worked way better.
A template might look like
Medium Grip Pulldowns
Seated Cable Rows
1 Arm Farmer's Walk
45 Degree Back Raise
Hanging Oblique Leg Raises
Chest Supported Row
A. would be your deadlift day.
B. could be your warmup on an upper body day, just some abs and back raises to practice driving the hips/glutes.
C. you could just do your squat workout, and make sure to finish up with some RDL's for hamstrings.