I think a lot of people have misconceptions regarding LS vs. locker. LS are made for the street and lockers are for off road. A LS will no doubt let you down when you need it the most, say if one tire has all the traction and one has none (one tire on the road and one on a slick shoulder). A 2wd with a locker (either selectable or automatic) will do well on and off road but maybe scetchy on an icy raod. Its a toss up but a 4wd with no traction aid and a 2wd with a locker will spin the same amount of tires.
Limited Slip is made for off road too. They are designed to provide equal traction to both wheels after a minimal amount of slip on one wheel has occurred. You can put one wheel on ice and the other on dry pavement and leave a black stripe on the pavement if you jump on it.
Lockers are for off road only due to their function being to "lock" the axles together into a spool configuration generally by an air powered piston. You need to have poor traction with them to allow slippage at the wheels to relieve the binding that occurs from going around corners. That same slippage makes them no good for ice covered roads because whenever you go around a corner one wheel breaks loose and slips.
Even though a standard 4wd will only drive one wheel in front and one in back it is still better than a 2WD with limited slip or a locker because there is often different traction conditions on each end of the truck. Get the rear end into a gumbo mud hole with just a rear drive and two wheels spinning will just dig you deeper faster while 4Wd will pull you out.
A couple of years ago coming back to California from Montana I had to drive in 4wd in a snow storm from East of Bozeman to Wells, Nv. being over 600 miles. I couldn't/wouldn't have done that with a 2WD no matter what traction device I had in the rear end. You can't beat 4Wd in the snow.
As far as the anchor, be sure and put a short length of chain or heavy rope on the back of the anchor to use to pull it out when you're done. A fluked anchor can dig very deep before it gets enough purchase to be of any help and often requires it to get hooked on a root or rock. Being able to pull it out backwards makes retrieval a snap.