Does anyone know if a bottom bracket / bearing kit exists for converting an bike that has external bearing cups (Shimano 6600 series) to an older square taper design bottom bracket?

I know this is a "backwards" conversion but I've got a old Specialized Allez frame with a square taper BB that I'm running as a single speed. It was my first bike and the shop I got it at sized me incorrectly (it's a 50 cm and I should be a 52 or 54). I also have a Trek Madone 5.2 frame (unfortunately just hanging on the wall) that is the correct size. Wondering if there is any way I can move my current crank over with a BB conversion kit rather than having to buy a crank and bearings.

Thanks in advance.