I managed to bork an integrator free plan instance - the 403 forbidden issue due to messing up the MFA settings.
Is there a way to get the instance back to a happy state so I can login again?
Unfortunately, there is no way to regain access to an Integrator Free org unless the org still has an admin that can login or an integration that make an API call to fix those MFA settings. You will need to sign up for a new org, as discussed in our article here