Can I simply roll out a new VM with the same name, IP Address and CDP / AIA configuration and carry on as though nothing happened?
these property matching is not necessary, since they won't replace dead root CA. Essentially, you have to rebuild new root CA, deploy it to all clients and then renew issuing CA certificate.
Create a new REQ file on the Online Subordinate, Issue it that REQ on the rebuilt Offline ROOT, complete the REQ on the Online Subordinate and carry on as though nothing has happened?
this is the way to go. However, at some point, issuing CA will notice that one of previous certificates cannot be validated because of expired CRL. You can't renew CRL for deleted CA. But you don't need to rebuild issuing CA completely, just renew its certificate. I would suggest to renew all client certificates after renewing issuing CA, so all active and in use certificates chain up to new and existing root CA.
Can I simply script the deletion of that expired ROOT CA cert on my servers and carry on - business as usual?
yes. But you do that only when new offline Root CA is completely deployed.