To use a 360, you need a 798ci HD SI, 898c SI, 898c HD SI, 998c SI, 998c HD SI, 1198c SI, or a new model that is Ethernet capable. The 360 is an Ethernet accessory.
When you connect an Ethernet cable to one of those units, it disables an INTERLINK connection.
Bottom line is "you cannot have your cake and eat it too"
If you want two units to share data and use a 360 also, all have to be Ethernet capable (excluding the 1197c SI since that is not 360 compatable). Then you would need the 5-port Ethernet switch to connect all of them together.