With the licenses and the SAN (shared) storage you have, the migration shouldn't require much downtime. After upgrading the storage system, you can either upgrade vCenter Server or install a new one, depending on your environment (e.g. supported SQL version, vSphere features like vDS, permissions, etc.). Once the new vCenter Server is in place you can then install the new ESXi hosts and add them to vCenter (in evaluation mode, since the CPU licenses are still bound to the old hosts). Depending on whether the new hosts can be added to the same cluster (compatible EVC mode) you can even vMotion the VMs to the new hosts without downtime, otherwise you will have to create a new cluster for the new hosts and migrate the VMs while powered off. Once the "old" hosts are empty, remove them from vCenter - which will free the CPU licenses - and assign the licenses to the new hosts. As a last step you may consider to upgrade VMware Tools as well as the HW version (virtual compatibility mode) on the VMs, which will most likely require a reboot.
Caution: Do not upgrade the virtual HW version (virtual compatibility mode) for vCenter Server to HW version 10 (5.5 compatibility). If you do this, you will not be able to manage vCenter Server using the Windows based vSphere Client anymore!
André