Just curious to know why are you using HCX for the migration ? It can be done via cross vCenter migration right ? In HCX it does complete copy via network, so you may not be able to save time.
Also since the storage is shared between two envt. I assume both setup might have common networks too. We had similar scenario and we picked one ESXi node as ferry boat and move the VMs to that ESXi node and remove the node from VC01 , attach the ESXi to another VC, then just do a vmotion to destination cluster keep the storage as same. So that it will be just taking time of copying RAM contents (just a vmotion) as storage remains same. Repeat the process and move VMs in batches. It should be faster when compared to HCX migration.