It's not a problem in regular turns, only at really slow speeds, when I'm weaving through an obstacle that requires me to turn the bars.

I guess you're riding clips and straps on that Bates and prob don't want to put clipless on such a classic bike. However, on my bike I have slight overlap even with clipless and am wearing through the shoes where the wheel rubs across them. It nearly took me off the bike the first time I clipped the wheel in traffic, but now I am prepared for it and just muscle through.

If the overlap on your bike is enough that you can't push the wheel over the clip then the techniques above all work. You can point your foot up or down, "wiggle" the front wheel through the turns so that you avoid toeclip-wheel contact or skip the back wheel to move your pedals. Since it's only at low speed you can stop, trackstand and wait for traffic to move as well.