In New Jersey, If You Evict A Commercial Tenant For Breach Of The Lease And The Tenant Is Evicted, Can You Still Hold The Tenant Responsible For Rent Until The Lease End Date?

This is not possible - a tenant will be required to pay all rent in arrears and all court costs in the case; and pay all losses or damages which landlord may suffer as a result of tenant remaining in possession.

Your plan to bill the tenant until you can re-lease the unit would expose you to liability, just be glad they didn't trash or burn the place down. Your only recourse would be to sue them for losses incurred due to the proven breach of lease.