If you want to minimize your lat and upper trap engagement and specifically build your mid back, then any kind of horizontal pull is your best bet. Close grip pulldowns with an exaggerated lean back, chest supported rows, neutral wide grip seated rows, pendlay barbell rows, T-bar rows. They all help develop mid back thickness, especially if you retract your shoulder blades during the pull. Heavy weight, with good form.
Carries, shrugs and so on will target your upper traps more than anything, same with snatches which require a much greater time investment to learn. Deadlifts or RDL's with straps are pretty great though if you understand how you engage your traps and lats before the pull. Facepulls are great for mid back definition and rear delts.
Try adding close grip pulldowns with a lean, neutral wide grip seated rows, T-bar rows, strapped RDL's and facepull x2 spread out during the week for the next two months and see if your mid back doesn't grow significantly.