Ugh. I feel your frustration. I do not have a narrow foot -- at least not the forefoot -- if anything, I think it's on verging on wide across my toes -- but I have a medium volume foot, high instep, and very narrow heels, and I can count on two fingers the number of pumps I've owned that actually stay on my feet (and only then with BARE feet -- never when I am wearing hose). Low vamp and even higher vamp flats and most sling backs pose similar problems.
My sole pair of pumps are Eccos -- I bought them 7 years ago and still have them and wear them. But that was a fluke -- because the other Eccos I've tried haven't worked. And I also have a pair of wedges by Vince Camuto -- those ones have elastic around the side and that's what holds them on -- as long as I'm not wearing hose.
It's probably no help, but I've essentially given up on open vamp styles. Even though they are far more flattering to my short calves. Oh, I will try them on if they appeal to me. I'll continue to keep half an eye out for styles that might work. But I won't go into it with a lot of expectation, because so far, I have always been disappointed.
Flats I don't regret all that much, because I don't really like wearing complete flats anyway. But I would like to wear a pump now and again.
My compromise this year is the Sam Edelman Okalas. That ankle strap will keep them on.
Diana (who has similar problems) found success with some Munro slipper flats. I don't know if a slipper flat is your thing, but they were a fall item so might be on sale now.
ETA: maybe my foot is narrower than I think because my favourite bootie is Stuart Weitzman. But not in a narrow width -- just in the regular B width. Such lovely shoes, though -- worth every penny.