There are a LOT of variables involved here.
Does the host allow hot-adding disks?
If so, I think it would it be possible to add local storage.
Whether ESXi would allow the use of the new storage is a different matter, but it's worth looking into it.
Is it feasible to migrate the VMs to another ESXi host, even temporarily, the rebuild this host from scratch?
If so, this might be the quickest solution.
It would require rebuilding from scratch, but you wouldn't lose any of the VMs whilst doing the rebuild.
Regards,
Grant