AWS keeps a list of vetted partners (business requirements, public references, case studies, good AWS relationship, etc) on the competency page.

You can see the different sorts of competencies here, in case your solution has a specific vertical or technology focus: https://aws.amazon.com/partners/competencies/

You would want to focus on the consulting partners for this type of engagement.

If you're not sure, it sounds like it's more of a migration use case and you can get a short list of folks here: https://aws.amazon.com/migration/partner-solutions/

If you know your AWS account team, they'd like to get that feedback. Otherwise my contact information is in my profile and you can email me and I can try to connect you to some AWS folks responsible for the partner as well.