You can 100% run VSC 6.2.1 and SnapCenter 4.0 in the same environment. And you can still use VSC to restore backups that were created in VSC. I've tested this and it works as expected.
There is another thread here, https://community.netapp.com/t5/VMware-Solutions-Discussions/Upgrade-VSC-from-VSC-6-2-to-VSC-7-0-Retain-backup-policy/m-p/137294#M9163, where we actually ran through the entire migration process of upgrading VSC and retaining backup jobs.
I have completed this for a few customers now and each has been successful.
If in doubt, create new jobs with SnapCenter as you suggested and wait until your existing VSC jobs reach your desired retention and then delete the snapshots (VSC only removes older restore points after a job runs, so you will need to remove the snapshots manually), and then upgrade to VSC 7.1.