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58cm does seem pretty tall for a guy that is 5'9". In all honesty, if you have not spent a bunch of money restoring this bike, then I would probably recommend you save that money, and buy a real fixed gear bike such as a Mercier Kilo TT, Windsor The Hour, or Dawes SST AL. Those would be a better choice for a fixed gear bike if you're really interested in this culture of riding fixed gear and you'll be able to buy a bike with a measurement that will be comfortable for you.

However, if you feel that you have put in a good amount of money for parts in this bike, then keep it and maybe find a used frame with track drop outs on craigslist and swap all the parts over.

Then again, if it was me, I would probably stop this project right away (or maybe wouldn't have even started it at all) since the frame is already too big for me and it's a conversion fixed gear.