If you can get the "Powers That Be" to agree to a vSphere Essentials license, then Veeam Backup Free Edition could deal with your migration situation.
Veeam Backup Free Edition for virtual machines (VeeamZIP)
It has a feature called Quick Migration that, in the case of vSphere Essentials where you don't have vMotion, would use Veeam's SmartSwitch functionality to migrate the VMs between hosts. It's not quite like vMotion and it does temporarily suspend the VMs, however it minimizes the time required to migration them as much as possible.
Further to a.p.'s comment about you being in a 24/7 critical shop, vSphere Essentials Plus would get you vMotion, HA and DP as well. Good luck!