Yes, indeed. Which is why thought of the 1:1 transformers to invert the polarity at the input.
There is a lot of off-topic discussion cluttering up this thread, but I think you should have lead with that. You are really planning on building a mix console with no active electronics? That sounds...challenging to me. You mentioned EQ, were you going to use old style LC EQ circuits like in a Pultec, but with no make-up buffer?