Well, it sounds to me like you might have a short that is causing the blow outs. Might want to check your wires starting with the trailer electrical connector(since that was when you first started having issues).
I also have problems with LOM but have all my lights working and have checked all wires, bulbs(correct bulbs), and fuses. I replaced the LOM and it still gives me the "rear lamp failure" message. Only comes on if I hit my brake pedal after starting up, if I drop it in gear without hitting brake it won't show up till I hit pedal, was thinking the brake pedal switch might be bad?