I suppose it depends how bad your toe overlap is. I actually get it on my geared CX bike as well as my fixed gear bike, and yea I can try to avoid it by turning the wheel when the pedals are verticle instead of horizontal, but I still get it frequently during slow speed maneuvers. I've found the more it happens, the less it bothers me. My toe sort of skims the edge of the tire, but it doesn't upset the handling in any way. I suppose if things were getting very tangled up it would be a problem.

Try to avoid it by timing tight turns so that the outside pedal is as far from the wheel as possible when you turn. for instance start a left turn just after the right pedal passes through the downward stroke. When toe overlap happens drop your heel a bit, and the tire will roll over the toe easier.