I've re-patched a couple of times now and this glitch just keeps happening.
The ship's layout is completely messed up. All the rooms are in the wrong places, they've all shifted one space to the left, and the doors are in the strangest places. I'm sure I've patched the mods in a non-conflicting order, but here they are anyways (in order):
Alpha - The sM Polish Kit for Advanced Edition
Better Planets and Backgrounds_v1.3.1
CE Resource Pack 1.261
FTL Captains Edition 1.262
CE BPaB Compatibility Patch 1.0
CE Additional Music Addon 1.248
randomFlagship
Randtrel
Patch - The sMPK for Captains Edition
Module - Augmented Weapons for sMPK-AE
Module - Augmented Weapons for sMPK-CE
GFX - Ship Greebles for sMPK - CE
Ship - Captains Edition Player Ships
Module - Enhanced Systems for sMPK
Here's a link to the mess. I've linked it instead of putting it on the FTL forums as big pictures get chopped off by the forum.
Running on OSX and patched with Slipstream Mod Manager v1.6.
Remember: You can never have enough lasers. Or beams. Or missiles. Or Ions. Or bombs.