Well, what kind of opponents are your Lights having trouble staying alive against? For most lights, they're not going to last long against, say, heavies or assaults. And even against other lights it's not going to be a pretty fight. Take the good old Stinger-3R. In a Stinger-vs-Stinger battle, only the front Torso sections can take a single ML hit without going internal, & none of them can take a 2nd one. Most locations (including the Head) are vaporized after 2 ML hits...bad luck for whichever pilot just lost their Right Arm & is down to a single MG, or just lost a leg (& good luck trying to jump with that hefty PSR penalty). If they're facing an enemy with an AC/20 (Hunchback, Victor, etc.), then the best outcome from a single AC/20 hit on the Stinger is for a hit on the Left Arm from the Forward Arc. Sure, the arm is gone...& so is the Left Torso...& you lost 2 points of CT armor...but you still have both legs (so you can move 6/9/3 still), & you still have your Medium Laser. Hitting the RA means you're down to a single MG for your weapon. Hitting either Leg means that Leg & the Side Torso are both gone (plus whatever Arm was on that side), so you could be down to a single MG and be essentially crippled (Movement of 1/2/3, assuming you want to risk the PSR penalty to Jump). Anything else that hits you after that (or in the same turn) is pretty much a death sentence.
Alpha Strike already mirrors that quite easily. A Stinger can take 2 hits from another Stinger before Structure is exposed & it starts taking critical damage. The only reason it's a little faster is because you're missing the possibility of multiple hits over multiple turns striking different locations. Against a Hunchback (Short) or Victor (Short/Medium), though, it's toast...the only difference being that instead of being outright crippled it's considered destroyed, but again since it didn't really matter where the AC/20 hit you in tabletop it's understandable.
Haven't tried DFA's Home Rules yet, but might take a look at them.
I do have an issue, though, with switching to a D12 instead of 2D6 for the rolls. Consider that Stinger duel example. Assuming they're in a completely open map (no terrain modifiers), & no modifiers for heat & damage, with a Skill Level 4 each pilot needs a (4 + 2 Attacker Jumping + (TMM 2 + 1 Jumping)) = (4 + 2 + 3) = 9 to hit the other when within 6", 11 (+2) out to 24". Rolling a 2D6, they each have a 10/36 chance (27.78%) to hit within 6", 3/36 chance (8.3%) to hit out to 24". Rolling 1D12 instead? Now it's a 4/12 chance (33.33%) to hit within 6", 2/12 chance (16.67%) out to 24". That's a 20% better chance of hitting the target close-in, & double the chance farther out. Better chances of hitting the target means combat is going to go even quicker...so if you think Light 'Mechs die too quickly in Alpha Strike, you're going to find them dying even faster by switching to a D12.