Hi Bret, I own both a 1962/63 Bianchi Specialissima and a 1964 Bianchi Competizione. Don't know what model you have, but the derailleurs on either model in 1964 would have been Campagnolo Record front and rear.
Here are the Flicker photo site addresses for both of my bikes in case you want to examine for correct components, as both of these bikes are 100% original including paint (don't forget to change the (at) to the @ symbol:
Specialissia -
http://www.flickr.com/
Competizione -
http://www.flickr.com/
Hope these photos are useful.
Regards,
Kevin Kruger - Grantville, PA