The thin lens equation might give you a starting point. I don't know whether the corrections required for a "thick" multi-element lens would be significant in this application. The equation is:

1/O + 1/I = 1/F

so 1/I = 1/F - 1/O

where O is the object distance; I is the image distance and F the focal length (all positive).

According to the Android app DOF Calculator, the hyperfocal distance for a 180mm lens at f/16 is about 17m assuming a CoC of 0.12mm. For an object distance of 1700mm, and focal length 180mm, the image distance (according to the thin lens equation) is 201mm. This means the flange distance must be 201-180 = 21mm further than for infinity focus, so 195mm if the flange distance for infinity focus is 174mm.

However I would probably focus closer than this, on the basis that some softening of distant objects is an acceptable trade for a closer near focus distance. Of course this depends on the application.