It would feel odd for my head to be out past the bars. Especially if you feel like you're arms are back behind you when you lean down a bit. I doubt that I could tap the bars with more than the crown of my head on any of the bikes.

Seems to me that if you're short of leg and tall in torso that a women's specific frame is what you need. Your build is quite common among women and a lot of the companies produce bikes with lower standover and seat tube sizes but that have long top tubes to suit the taller upper body. And NO they are not step through frames... Check out the companies that have the separate lines for women and check out the geometry and sizes. I'll bet you can find one that is a slightly lower and longer top tube than you have at present.

I know it seems like a PITA when you're otherwise happy with your bike but when you're built a bit different from the "norm", whatever that is, you gotta shop a bit more carefully. Sure a longer stem will sort of make it fit but with extreme long stems comes slightly funky handling which would be nice to avoid. So measure up your present bike and study the frame geometry charts looking for a slightly shorter standover and a longer top tube.