I don't have a Sav/Inv Stalker, but I do have each of those powersets paired with a different primary/secondary. I put them together and ended up with the below which looks to match the defense, resistance, health, end consumption, recovery, etc.. of your original build but eeks out another 30%-ish global recharge and moves more damage to AS rather than Zapp.
There may be room to proc out AS more but when I tried to shuffle some of the slotting I couldn't see a clear path to soft-capping Nrg/NE (ended around 43%). I'll probably keep poking around to see if that is possible though.
Edit: Figured out one way to get more procs in AS (and Zapp). It costs a fair amount of global recharge (-17.5%, down to 155% total) and Savage Leap is barely under 95% chance tohit at +4, but based on your original build neither of those things may matter as much to you.
Stalker (Savage Melee - Invulnerability).mbd
Stalker (Savage Melee - Invulnerability) - Procd AS.mbd