Have you tried pulling your handbrake on half-way?  That's all you need to do for temporary LSD-like action, and it works every time.  (This is assuming your rear brakes are in good condition, and brake cables are acting evenly between the two sides.)

 Date:    Mon, 1 Jan 2018
 22:37:58 -0600
 From:    Stephen Edwards
 <chibicyclist@GMAIL.COM>
 Subject: Locking differential
 
 Vanagon list:
 
 What's the verdict on lockers?
 I ... occasionally need to pull
 a boat out of the water. The 
 place where I go has a sandy beach and
 the rear wheels get stuck every time.