Yeah.....I think most people that have done this swap are merely replacing their open R180 with an LSD R180, which avoids the issues you're running into. The input flange from any S30 R180 "should" work (i.e. I don't believe it needs to be from a 240Z).
And yes, the shorter R180 would nominally require a longer driveshaft than an R200. However, keep in mind that Datsun moved the differential rearwards in the middle of the 240 production years (I think between '72 and '73). This change improved the half-shaft angles, but resulted in a different mounting position for the diff.
What year is your car?