Phase inverting problem

Hello,

I have a Conrad Johnson PV-12A pre-amp. It is phase correct for the phono stage, phase inverting for the line stage.

My power amplifier is a conrad johnson MF2100. It is phase correct.

So my first idea was to connect the speakers to the power amplifier the wrong way (black to red, red to black) and then connect the cartridge the wrong way around as well (R: + and - reversed, L: + and - reversed). Then the phase should be correct for everything.

But there lies the problem. When I switch the connections on the cartridge, I get a really loud hum, makes the music barely hearable. Perhaps it has something to do with the fact that R- is connected to the cartridge body, it is some kind of earth? Anyway, switching the connections on the cartridge is not an option. So, what to do?

My only idea so far is, seeing that I only have one line input (cd), is cutting open the RCA cable and switching + and - of the line, and connecting the speakers to the power amp the correct way. So, I'll do just that. But maybe there's a better solution that I'm missing. Any ideas?