Are you using more vendors than just Meraki switches?
If you are using Cisco Enterprise switches, configure them to use mst.
spanning-tree mode mst
If other vendors use single instance RSTP, use that. If they create a spanning tree instance per VLAN (like Cisco Enterprise) configure them for MST instead.
Ports between switches should be configured as trunk ports. Ports to end devices should be configured as access ports.
A convergence time issue is 99% likely to be due to the configuration, rather than a cable fault, in particular a uni-directional cable fault.
Chances are if you follow the above you will get rid of your convergence time issue.