Smittie, we're foot cousins. I have a regular width forefoot, but a high (ish) arch. Not a super high volume foot overall, though. And a very narrow heel.
Pumps and flats (even higher vamped loafers and most slip on sneakers) never stay on my foot.
Certain brands are better and certain ones are worse. Clarks and Naturalizer regulars are too wide for me all over.
Ecco sometimes works, or works with an insole (depending on the shoe) but booties or tie ups, like sneakers, are pretty much my only option other than sandals or sandal booties. I've only ever had one pump that stayed on without straps and it was an Ecco -- but most of theirs don't stay on. I have read that they and Munro and Stuart Weitzman and a few others do have a mixed last (heel and forefoot different) but I'm not sure if it is true.
It also helps me a lot to wear EU 37 vs. a US 7. Some US 6.5 fit in the length well but are a touch too narrow in the forefoot (it just depends) whereas the EU 37 have a better chance of working. UK sizes don't work well on me.
You might experiment among brands that way a bit and see what works best for you.