You will be wasting your time, by trying to shim the spider gears in hopes of making it more of a posi.
Your choices are...
automatic locker (like a lockright),
a limited slip (probably best for what you are wanting...but very hard to find...I don't know that anyone sells them new anymore...so used is what you are left with....and I have only seen a couple for sale, ever),
a spool (permanently locks the axleshafts together),
an ARB (a selectable locker, but you are looking at big $$$ and gear setup),
welding the spider gears (cheap, but most fail over time, and it is basically like a spool),
leave it open and live with decreased traction.