The main problem is unbalanced input, which prevents you to add the switch. 4-pole switch in one position will connect shields of cables to non-grounded pins of the inputs, so you will have big hum.
If there is the need for rotating phase, you can build a simple stage and connect it between the output of Cornet 2 and the input of the following preamp. The level of signal is much more in that case and the switch has less impact.