Thinking well, it hasn't has to be so difficult. I could desolder it and solder to the other side (would be better to put one with an angle).
The socket pins are staggered in a way that means they won't physically align with the holes on the reserse side of the board. I've not seen any sockets available recently which will suit what you want to do, but mirroring the existing socket will not mechanically work. Draw it out on a piece of paper to test the theory.
I'd agree with the other comments that it would surely be better to find a SIMM that fits!
