We are almost the same size...
But a lot depends on your build. I have longer legs and a shorter torso, so the 62cm Treks (rode a 5200 for years) are actually a too small for me. I rode a VERY long seatpost and had more drop to the bars than was really comfortable.
Most bike shops will not be stocking 62 or 63 cm frames, because they are not in demand. I had to call around and find a shop that even had one in my size. Some will have one shipped in, but only if they believe you are going to buy it if it fits.
My best recommendation is to spend a few $ (usually 75-100) and get a fitting by a professional at a LBS. May seem like a lot, but they will be able to confirm the sizing you need for a frame. In the long run this will save you a lot. Once I had this done, I realized the 62cm Trek was too small, and then opted for a nice Cannondale 63cm which fit much better. You can also use a fit calculator online (Colorado Cyclist, Zinn, etc.), but if you are not flexible these usually won't take this into account. You would be better off having this done in person by a professional.
The bottom line is you are not of a size that the bike manufacturers are building for, unless you go custom (which I did). You are going to have to work harder to make sure you get a bike that fits you. The bottom line is the right bike is the one that FITS, not the one that is prettiest, has the best spec, etc. If it doesn't fit you won't be happy or comfortable.