Pinching your shoulders together will tighten your traps but the lats are more important for providing a stable load path through your mid section. You want that to be rock solid for all your training reps so the bar path can remain constant.
I think you should at least give the band a try and lighten the load on the bar. When I first tried to fix this problem, I still had my shoulders slightly shrugged back while trying to rotate my elbows and it didn't work that well because the tightness was inconsistent. The purpose of the band is to prevent any scapular retraction which allow for a more natural tendency to move the elbows forward. So don't throw that off the board unless you've tried it with the bands and it still hurts.
If that doesn't work, then you would just end up pulling the elbows down as best you can like a lat pulldown while the shoulders are shrugged back to engage the lats.