Server 2016 MSMQ failover

From my experience, MSMQ deploys find on top of clustered shared volumes. Therefore, any software shared solution that does mirror/present storage to Failover cluster as CSV will do the job.

I can recommend you try HPE VSA, StarWind VSAN, Microsoft Storage Spaces Direct, so far all of them do share nothing storage for Failover Cluster. I would suggest StarWind in case you don't run Hyper-V on your hosts, so it will do free mirrored storage.

You can also stick with Always On scenario that doesnt assume a shared storage and where the overall health of your cluster would be determined by the votes of quorum of nodes in the cluster. But this feature is an enterprise one. So in case of tight budget, I would also recommend to go with FCIs.