First - I tried the ice trick; actually, I used a flexible freeze pack since it wouldn't melt and is purportedly colder than ice. Wrapped it in a light cloth and molded it around the shoe and left it sit for a while. when I came back to it, the gum was definitely brittle but since it was such small strands I just couldn't get them to come off the leather. I got a couple of plastic collar stays which seemed like soft enough plastic to pry the gum but not hard enough to do any lasting damage to the leather, but to no avail. In retrospect, I think if I had tried it when the original blob was on the shoe - before I got most of it off and left all the little strands - I think it probably would have worked and popped the whole thing off in one go, but alas.
So, after reading more online, I manned up with the goo gone. I started small (squeamish, me) but eventually got a good dose of it on there. I tried rubbing with a cloth, trying to pick it up, but that didn't seem to be working. After a little more surfing online, I stumbled across the idea of using a toothbrush. I grabbed a spare from the closet, made sure it was soft bristles, and using it in strokes in a single direction, I slowly worked it off. I added a couple more drops of goo gone here and there along the way and, viola, all gone.
The goo gone doesn't appear to have marred the leather's actual finish (whew; that was my biggest concern) but of course it took off my wax job. Time for some saphir, wax, and elbow grease.
Hope these tips help someone else in the future!