For this case, you're right -- the Instance ID would be the way to go. On the new BuildMaster server, you can set the Agent.InstanceId field (any string is fine, "bm62" would work) , so this way, both BuildMaster instances won't collide.
We are using our "Customer Success Program" to provide upgrade assistance for BuildMaster 6.2, so the best way to get started on this would be to talk to your account representative.
You can also submit a ticket and put 6.2 UPGRADE in the "How can we help" section, and we'll route that to the right people :)