I have to do that with my 35mm (actually 32mm) tyres, but it's a faff, I'm back to using 28mm tyres which just squeeze through, esp when toeing in the pads steals a couple more mm.What I do is let the air out completely before I remove the wheel and then I always manage to squeeze it through but I do it gently.
It's the pads which catch on the forks/seatstays and prevent the arms "flipping" wide open, so unfortunately washers wouldn't alter that.Have you got more than one washer on the pad side of the arm? If you have, could you remove one and still meet cable set up criteria?