This is where vlan and layer 2 switches would be required IMHO. The phone system vlan would be shared and tagged. User ports would only have their data vlan untagged and phone tagged. Server etal devices would only have the data vlan untagged per company. The connection between the 2 companies switches could only have only the phone vlan.

If you have the option, LLDP MED to give the phones their vlan info would work for most devices in leiu of DHCP.