Solution 1:

The HP LeftHand implementation guides specifies links between the switches.

I have found that during high load, the links between the switches requires about 1 link per 2 nodes. Since you have 6 nodes, that would be 3 links for you. However, I tend to +1 when possible (to guard against port failure, allow for recabling without reduced performance, etc.) so 4 would be my final suggestion for you.

Solution 2:

vMotion migrates the active state of the virtual machines, it does not migrate the virtual machine disks or configuration files (unless you're using storage vMotion to migrate the VM storage to another datastore). As such, the source and destination hosts need access to the virtual machine disks and configuration files, which is why shared storage is required to migrate a powered on virtual machine to another host.

What I see as a possible workaround would be to connect one host from each realm to the other realm's shared storage (rather than connecting each realm's switching infrastructure). This would then allow you to migrate virtual machines from one realm to the other using these two hosts as "placeholders". When migrating a VM you would migrate the VM first to the placeholder host and then perform a second migration to migrate the VM storage from the source realm datastore to the target realm datastore, both of which the placeholder hosts have access to. From there you can migrate the VM to any host in the target realm. Since each placeholder host has a connection to each realm's shared storage this should be do-able without powering down any of the VM's.

NOTE: I don't have an infrastructure like yours to test with so I'm merely visualizing how it might be done and I think this method might work.