Hey bud,

I don't have the same experience as you, but it took me a month to learn how to pick differently. I left the Jazz III picks and went the Ernie Ball prodigy. Mainly because they were so small I would always play with my hand closed.

I like the shield picks, 1.5mm. Their much bigger and stout than the Jazz III at 1mm. The shape and tone is crisp and the attack is diffrent.

Pretty much what I did was set up the metronome slow and began just down picking for a few bars. I would stop, check to make sure my hand was still tall and my attack was good, and my hand didn't move from the bridge and continue. Then I mixed different picking styles and fragments of scales in every other bar till I got faster and cleaner. If I noticed my hand would get close to the strings or my hand would start to close again, I would reset my hand on the bridge, stand it tall and continue. After a week, I was able to increase the metronome speed 2 BPM every day. Now I gallop faster than ever and can play 16ths at 140 BPM. Im just getting faster, but I deliberately practice about 20 minutes a day just picking. I am willing to share my practice routine with you if I may. That includes light, medium, and heavy palm muting, that I had to re-learn when I changed how I pick. 

I think Jazz III picks have a place, but for me, I would get too close to the strings and not anchor my hand appropriately because they were so short. My palm mutes were inconsistent and my attack was weaker with a closed hand. And yeah, I still play with my hand closed but only when appropriate. So, now I can go back and forth between open and closed as required. 

My thing works for me, it's just boring after the first three weeks. So, I do the routine only about three days a week now. It wouldn't hurt. I can upload it for you tomorrow in a link video tomorrow after work if you're interested so I can explain everything. Also, the website allows you to upload videos for instructors to coach you as best they can. They're obliviously more qualified to diagnose your hands than I am. 

Be safe, brother.