I'm not really sure why you would armor an arm with no weapons in it. Once it's destroyed, its taken out of the hit tables, maning that shots from the front actually have less chance to hit your left side. Armoring that arm means taking away back armor, which means that it would be far more efficient just shooting you in the back anyway.
Actually brace does not work if you are attacked from behind. The tooltip specifically says front and side armor. Besides, you need all that back armor for when you jump into the enemy team and get back shots on them (thus showing your back). It's not worth using it to abosrb damage.
Lrm 20 with breaching shot seems like a good idea, but 2 issues with that. First, breaching shot is a gunnery skill. Their are no high gunnery, high tactics pilots. Shooting missiles mostly is indirect fire, and thus your breaching shot Lrm 20 is likely not going to be very accurate unless at close range, which defeats the point of lrms. Second, a single lrm 20 is not very much damage, especially when spread out over your whole mech. A bigger threat is if they have 2 breaching shot PPCs on Vindicators or Cicada. Very hard to catch and do good reliable damage to you (and to hit chance penalty sucks).
1. If by "being take our of the hit tables you mean no transference you are correct, but if you mean the percentage to hit LT goes down, that is just wrong as all locations except for head become EASIER to hit.
2. Forgot about Brace not working on rear. That said, you need to work on positioning if you are allowing rear shots on a regular basis. You could half the armour there and get some of that on that Left Arm and use it as an actual sponge rather than a 2 ML "buffer".
3. Who said anything about a single LRM20?