An alternate (but potentially more difficult) method to solving OBB vs OBB collision is to transform one OBB into the space of the other, such that one of the OBBs becomes axis aligned.
Basically you translate the two OBBs so that the center point of one is at (0,0) then rotate the two around (0,0) until the OBB at (0,0) becomes axis aligned. You can then use SAT to resolve the collision, but all resulting values will be relative to the current transformation (and thus you'll have to un-rotate around (0,0) and un-transoform)
tldr; Linear Algebra + SAT