I don't understand how this was helpful but then it just may be me? But no, the crank manufacturer does not dictate the length of the bottom bracket spindle, though they may give a recommendation. One of the "benefits" of the old square taper cartridge type bottom brackets was the ability to adjust the chainline, which was essentially what the OP is asking.

As to length, while the overall reduction in width between a 127 mm and 113 mm BB is 14 mm, this is split evenly between the drive side (D) and non-drive side (NDS). So your chainline would be reduced to 49 mm (56 - 7). The typical chain line for a road double crankset is 43.5 mm, as measured between the center of the seat tube and a point halfway between the two rings. Note that your method of measuring chainine is not standard (see
https://www.sheldonbrown.com/chainline.html).

Before you buy a new bottom bracket, measure the space between the chain stay and the existing small and large chain rings. I don't know of a minimum clearance but you don't want to install a new bottom bracket only to find your chain rings hit the chain stay.

Karl