Preventing network loops with secondary core switch

Good Morning, Everyone -

Working on a project to add a secondary network core to our infrastructure, to eliminate our current network core as a single point of failure - see diagram here.

Currently, I'm trying to figure out the best way to prevent network loops in this topology. I know I could leave it to spanning tree, but that doesn't seem like an ideal solution.

My two current core switches, and my DR core switch will be Nexus 9000's with L3 functionality, but my distribution switches are Catalyst 2960's with L2 only.

Any input is appreciated!