Account Linkage - How to change

I have an implementation where when Eloqua was originally set up, they performed the Contact to Account linking based on a unique identifier from one team's CRM solution. Usage has since grown and the rest of the company are now using Eloqua, but the majority of their customers aren't on that original CRM solution so most accounts and contacts aren't being linked as most of them no longer have a unique identifier in that field.

Everything indicates that Account linking isn't reversible (i.e. you can't change it to a different field), but would we be able to change the contents of the fields to a new set of unique identifiers and have them link up (e.g. replacing the unpopulated CRM IDs with Eloqua IDs)? Has anyone tried this at all?