Replaced Shimano Bottom Bracket, now front derailleur won't shift to largest gear
Despite the the spindle length is 113, but as you observed, the offset is different - so the cranks are sitting in different positions. Not all Shimano BB are made symmetrical - and UN55 BC 1.37 x 24 113mm. means its a 1.37*24tpi thread, with a 113mm shaft - not mention on the offset of the shaft. Based on all this, evidence is that you have an imcompatable BB. 

Presuming you have correctly refitted the crank (so it is seated properly) - What to do about it - best would be to go to a 110, or even 107 mm BB - this will move the crank to the centre of the bike and fix the problem, also providing better alignment. 

Alternatively, are you certain the derailleur won't move out further. Best thing to do it unhook the cable outer from the frame (or shifter) so the cable is certainly free and not stopping the shifter moving to it's outer most position, and release the outer limit adjustment screw on the derailleur. If the derailuer then moves out far enough, you should be good to set up, as it's "just" adjustment of cable and limit stops. If not, you will need a different BB. 

It is not possible to install the BB backwards - the right hand side has a left hand thread....... 

Edit: In response to OPs comment..... 
The problem is then to do with the BB getting to the correct chainline - MTB sets should be about 47.5-50mm. If you cannot find the correct sized BB, and a 110mm is too short for the left crank, you have two other options - try a different left crank, or (Perhaps for the really desperate only) I have seen this web article about grinding off the lip on the fixed right hand side, allowing you the thread it into the frame further, thereby to give the ability to adjust the chain line. (I would get a local engineering shop to use a lathe.....)