I'm only 5'-10" (178 cm) now, but have, apparently, long legs/high waist and I also prefer to pedal "toes down". I'm perfectly comfortable riding a 63 cm frame with a bare fistful of (Campy two-bolt) seat post exposed, especially since I like how I can use a normal stem and get the bars nearly level with saddle top. But that's just a preamble:
When I first built a "performance" bike back in the mid-80s, I was advised to get a 57 cm frame because that was what people my height should ride. I did that, and loved the ride of that frame -- but I realized slowly that I needed/wanted a higher saddle (and bars, even moreso as time wore on). So I adapted: got a Sugino "Crystal Fellow" seatpost to replace the Campagnolo Super Record that was shorter, and a Nitto Technomic stem (the ubiquitous 7-shape). That worked well, but I hated the looks of what I'd turned the bike into. The stem, in particular, was offensive. Then I bought a Nitto Dirt Drop stem (more an apostrophe shape), which, if one looks, is available in both 80 and 100 mm reach (though you can't be choosy about bar diameter). That made a much more satisfying presentation, which I have recommended to others who had the same issue.
Eventually, in buying vintage frames, where the availability of 63s is quite a bit better than 60s or 61s, I ended up where I am. I do have a few 60, 61, 62 cm frames, and even a 59.5, but (I seem to collect these things) have ended up with several 63s, one of which is my daily rider. (I'm somewhat ungainly mounting and dismounting, but stopping/starting is no problem at all.) I realize that, in order even to make one of the project frames in the 60-61 vicinity work for me, I'll need to use one of those Dirt Drops. I have no problem with that.
Long and short of it: suggest you work with what you have rather than starting over.