I have three comments to make before I get back to work:
1. THe Shimano wheels are probably not the best option for a big guy. More spokes = more strength (if the wheel is properly built), and the Shimano wheels are low spoke count wheels.
2. Are you sure the bike is a good fit? and old 60cm frame is probably 1 or 2 sizes down fromt he largest size made in any model... the equivalent to a "L" size bike.. maybe a "M/L." You are 6'4"... if they didn't make the largest (or second largest) size bike for people 6'4" then who did they make them for?
3. If the tires say 27 X 1 1/4 then they are probably not tubulars (also called 'sew ups,' have an integrated tube, are glued to the rim), they are probably 'clinchers' (separate $5 tube and tire not glued to the rim)