I've done things a bit differently:
At the core we have 2 x Catalyst WS-C3750X-24S, which is the existing core switch stack, and remains that way for the time being. So the Meraki network is currently sitting off the edge of the Catalyst core, utilising 2 x Ten Gigibit SFP's.
The Catalyst stack and the whole of the Catalyst network is utilising Rapid PVST (Rapid Per VLAN Spanning Tree) and this Catalyst Core Switch Stack has a Bridge Priority of 8192 (architecturally, this bridge priority was intended rather than 0 purely so that it would be possible to slide in a higher bridge priority device if needed, anyway!)
The Meraki's comes into play..
We have 2 x Meraki MS425-32's connected via 10G SFP etherchannel to the Catalyst Stack's TenGigEth ports:
MerakiMS425-Switch1 / 32 <> Catalyst Te1/1/2
MerakiMS425-Switch2 / 32 <> Catalyst Te2/1/2
Goes without saying, this link between the Meraki Stack to the Catalyst Stack is Aggregated.
The 2 x Meraki425's are stacked via 40GBASE-CR4 cables for redundancy if either of of the aggregated pair breaks.
The Meraki 425 Stack is set to use RSTP with a Bridge Priority of 12288, and all Meraki Edge Switches use the default bridge priority of 32768.
NOW! The important bit:
Rapid PVST only passes BDPU's across the default (VLAN 1). Because Meraki does not support Rapid PVST, we have chosen not to trunk VLAN 1 on the etherchannel connecting the Catalyst and Meraki Stacks. In effect creating two segregated STP networks, but allowing all other VLAN's other than VLAN1 to trunk traffic end-to-end.
The meaning of all this:
With this RSTP config, the Meraki 425's are the Root for all Meraki EDGE switches; and,
The Catalyst WS-C3750X stack is the Root for all Catalyst EDGE switches.
If by chance/mistake the Meraki Network's STP does converge with the Catalyst Network's STP, I'm hoping the higher bridge priority on the Meraki 425's somehow will instruct them to not take over bridge priority from the upstream Catalyst stack.
This is as close to the ideal scenario I can get to without reconfiguration Rapid PVST on the Catalysts to use something more standard/supported by the Meraki's.
We do have plans to remove the Catalyst Edge Core at some point, but for now it is needed because it is doing some fancy BGP stuff that I haven't got my head around yet. The Catalyst Edge switches have had ALL of their end-devices migrated to the Meraki's. So from a edge distribution point of view, the Catalyst Edge switches are sitting there doing not a lot.
Sheesh, I hope some or all of that makes sense.