Yes I've come to the conclusion it's just how it is.
I've spent a couple of days with the receiver in pieces trying to see if I could get rid of all the crosstalk and noise. No luck, but I made some interesting discoveries:
I found that when using the continuity test on my new DMM, if there is an audio signal, I can hear it playing through the DMM.
I wanted to be sure it wasn't the switches causing the problem, so I took apart the most likely culprit (the aux selector switch). I was pleasantly surprised to see it was very clean and shiny inside. So at least I can be fairly confident all the switches are clean. It was quite easy to get inside - I had de-soldered the pins at the bottom, but then realised I didn't need to. I've added a couple of pictures below if anyone is wondering what the inside looks like.
I disconnected some of the different stages to see if I could isolate the problems. It's actually not that difficult to unwrap the wires around the pins, and put them back after. Regarding the noisy phono inputs, I found that if I disconnected the inputs completely at pins 3 and 5 on the equaliser board, it was still just as noisy, so I guess it is just the level of amplification done by the equaliser board (and not something picked up by the input jacks or wires to the board).
I managed to eliminate the aux left channel leaking to the phono inputs by disconnecting the aux input wire at pin 17 and connecting it directly to the appropriate aux switch pin (I also took the 100k resistor off the board and put it between the wire and the pin). I've included a picture below. Like this, even at full volume I couldn't hear anything on either phono input (and it did play fine when I selected aux).
I've cleaned the board - especially round that track and all round the pins, but I can't see anything suspicious. I'm just assuming it's because the pins are so close together? And it is specifically the left channel from the aux source playing through the right speaker on the phono input, and it's about twice as loud on phono 2 than phono 1.
I put it back how it was, I'm not ever going to have aux playing at the same time as phono so it doesn't really matter anyway. And I think it'll be better to use the tape input rather than aux, since that skips the switch assembly board all together.