I am exactly one inch taller than you, but with the same exact cycling inseam. I have always had the same issue you are facing. My current ride is a 2007 LeMond Buenos Aires Min-Max carbon frame bike. The way I partially solved the issue is to use a 90mm stem. Even with that, there is still quite a bit of seatpost showing, but the reach is spot-on. The drop is not bad, but I am quite flexible.

I think a custom carbon frame will solve the problem quite nicely, but I have not seen an affordable carbon custom house yet. Still looking though.