It isn't a dangwer at high speed because you can't turn that sharply when going fast. It will only happen when going pretty slow---basically during u turns and that kind of thing. Just learn to live with it; to reduce the chances of it happening, learn to time very sharp, slow speed turns with your pedal rotations, and point your toes up or down.
It's very easy to get used to. My first conversion had some overlap, and I have especially large feet, so of course I have large toe cages as well. I still use that bike with a set of fenders, meaning I have another inch or so less of clearance and have no trouble.