Your choice of spindle length will depend on the crank you choose, as well as the width of your bottom bracket shell.

122 mm for a double just seems weird. Generally, I've been fitting 122 mm spindles to inexpensive MTBs and hybrids with 130 or 135 mm hubs, 73 mm BB shells, and Shimano or Suntour triple cranksets. There are a couple oddball Suntour MTB cranks that take conspicuously shorter cranks.

The 110/113 mm spec for the double most likely implies 110 for a 68 mm shell, 113 for a 73.

Shimano's data sheets (online and and included in the crankset packaging) are usually pretty thorough about spindle lengths with different applications. Your application, 68 mm shell with a 130 mm rear axle, is pretty standard for road bikes. You could do an end-run and simply get a new Shimano Hollowtech II (Tiagra or R500, maybe) or FSA Mega-Exo (Gosssamer, etc.) crank with outboard bearings.