Sendmail migration help

I am currently trying to move away from an old email server to Google mail for business. As email is critical for everyone in the company we are trying to do it gradually to minimise the risk of emails getting lost or something going wrong.

Our existing email server uses sendmail 8.13.8 as the MTA. We also have MX records for the domain pointing to this old email server. We have a google mail inbox but it currently receives nothing as there aren't any MX records pointing at it.

We are hoping to set up some sort of forwarding system so that our users can be migrated gradually. The idea would be that when someone sends a user an email, the mail server would either deliver it locally (as it currently does) or forward it to the google mail server (that has no MX record) to be delivered there depending on whether the user has been flagged for migration. We could then gradually test the system with a few users and give them a chance to copy their existing mailboxes over to the new storage before we finally switch the MX record over to Google.

Does anyone have any idea if this is possible and how to go about doing it?
If anyone has any better ideas about doing this migration I'd also love to hear them.

Thanks in advance!
James