I'm in the 3-4 skull level of the campaign and have a mixed set of Assaults at my disposal. Two Highlanders and one King Crab, but looking for a replacement for the stock Battle Master or brawling Banshee (ugh) that usually makes up the fourth horseman of the apocalypse. (Actually been using an Orion quite frequently as a 4th.)

Accepted an Assassination Mission in the hopes of scoring an Assault. Took the super long way to the target area and that let me kill off two full Heavy lances without any issues. And then what comes strolling down the hill full of scree fields all by himself, but a Stalker. Yes! Finally an Assault that might meet my needs.

Wanted all three pieces, so proceeded to hit the Stalker with barrages of stability damage from most of my units. Pretty much every unit on my squad (except the dual AC20+++ wielding tank / King Crab) has a big LRM rack with extra stability damage and direct fire weapon with +20 Stb damage.

King Crab jumped closer and closer (and then entrenched to serve as a damage sink) while the others kept knocking the Stalker down. We knocked him down four times and got one head shot injury from the King Crab for the pilot incapacitation. Boom, a complete Stalker is mine. Never fired a laser except to try for a called head shot. :)

lucky, all my mechs carry a LRM15/20 and i've got a dedicated missile boat but i never seem to be able to kill a pilot with 4+ hp before the centre torso explodes

I definitely got lucky. It's way easier to knock 'em down once and then just core them as they lay on the ground. But then you have to hope you meet the same mech type in multiple missions. I'm still at the point in the campaign where enemy forces rarely have an assault mech, so seeing two of the same type on different missions is asking too much.

Why not pull off their legs when they're down? That'll almost always leave you one additional piece of chassis salvage, compared to a cored enemy. Open with a Precision Shot from your LRM boat (Stalkers are really excellent for that role, Highlanders aren't bad either) focusing on a leg and you'll either get a double leg kill, or if you're lucky, a pilot kill while the enemy is bouncing up and down.

Depends where you are in the game I think. Once I had Assaults / Heavies with LRMs mounted everywhere, it seems this is my preferred pattern:

A - Two mechs worth of LRM++ fire (80 missiles) that scatters damage leaves 'em on the ground. This doesn't cost the morale of a precision strike.

B - Then you have 'em on the ground and can hit 'em with whatever weapon you want. Usually it's 90% odds to hit the CT and 62% to hit a leg. Knocking one leg off is pointless since they get right back up again.

During the middle game when I was rocking Medium mechs, I couldn't do enough stability damage to knock a mech down. At that point, I followed your plan and used lots of precision strikes to take out legs. With one leg gone, it was more efficient to take out the other leg than go for the Center Torso.

So not disagreeing with you at all, just saying I think the two strategies apply at different times. But that's my experience and everyone has their own. :)

In my Assault harvesting scenario, I was trying to maximize my chances of getting all three salvage pieces. I definitely don't trust my head shot ability for that. And I wasn't really worries about counter attacks at all so I had the time to just pepper the crap out of the enemy with buckshot...