I wonder if there is a market for selling GDPR compliance / advising services. Some company that makes sure your doing everything right, and inspects the requests for validity.
I'm not aware of any willing to take on the liability of verifying identities as part of that, though.
Furthermore, even if you outsource the whole business process that handles sensitive data, you're still the 'controller' of the data, and you still carry full responsibility for it - you can and should have legal arrangements with the processor to recoup your damages/costs if they screw up, but you're the party that's directly liable, and if the processor can't/won't pay, that's solely your problem.
You can outsource certain parts of GDPR compliance - such as handling the paperwork and managing the customer enquiries properly, but it's hard(impossible?) to separate "the whole process" from the rest of your business.
What they do is somewhat similar to consulting and audit companies - they'll go over your internal processes and/or suggest standard procedures if you don't have any; they'll generally consult with the local data protection authority on particular interpretations and apply them to all their customers, etc. Creating/adapting a procedure for answering customer requests for their data (including the identity verification) would be part of the service; another common service is doing GDPR-policy training for e.g. call center employees. So a thing like that already exists; they won't take over your liability or your processes but they'll review your processes and hand-hold you through any adjustments needed.
they definitely won't be held liable per their contract nor handle the verification for you, but they do provide a system (a ticketing systems really) with a set of workflows that help put an identity verification system in place. It's nothing magic, but it definitely helps the privacy lawyers and DPOs who will end up bothering you with verifying all the data and providing it if needed.