Thanks for the comments, everyone.
It's not so much a problem of them slipping down my nose, like croakies would fix. I have this issue even when they are pushed up all the way. I definitely get what you're saying, old's'cool, about the vertical dimension of the glasses. That's something I was struggling to describe when I wrote the original post. Mine aren't quite granny size, but they are relatively narrow top to bottom. I'm surprised to hear that you can comfortably see ahead with glasses and that much saddle-bar drop.
Working on a straighter back may help, and is probably a good idea anyway. The stick-on nose pads would help, I think, but it would be good if I could use the glasses in normal fit when I got to work. I'd prefer to not have to raise the bars, for a few reasons, but otherwise that would work. Any other ideas would be much appreciated.