There is a whole lot of science behind proper rigging gear and technique. There are whole books written on the subject. I have had a career in the rigging field. Most of the work I have done required unknown load weight so estimating loads, friction and safety factors were key to not having surprises. Early in my career, my best friend was killed in a rigging accident on his job site. His nickname was Mr. Safety. Safety means learning and following all the rules even when inconvenient. Here are a few of my tips.
1. Try to have your sheave(s) the same size as your cable or rope. Proper sheave size reduces wear and damage to your cable or rope. The item you liked to is 3/4". Is your cable 3/4"? If you use a 7/16" cable in this 3/4" sheave and pull hard, you will flatten the cable in the sheave and cause extra wear to your cable and premature failure.
2. If you are using 2 double sheave pulleys I like to have 1 pulley have a tail hook. This pulley is attached to the load being moved.
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3. Keep all of your lines as parallel as possible to maximize mechanical advantage.
4. If you plan to use double pulleys make sure you have enough cable. You will need at least 4 times as much.
5. Always minimize bend radius. Cables and ropes do not like sharp bends. Large diameter sheaves will reduce damage to your cable or rope. If you tie a knot in a rope choose knots with minimum bend radius. Example, clove hitch instead of bowline knot. Make sure the knot is appropriate for the use. You cannot use a clove hitch in all applications.
6. I always do what I can to first minimize friction for the most efficient pull.
7. Learn the difference between force multiplication and force redirect. This is often misunderstood and this can cause a lot of headaches.
8. Make sure you know the working load limit (WLL) of all the components and do not exceed the lowest component in your system. You should just forget about the breaking strength. I try to never even get that number into my head. Most quality manufacturers will engrave WLL on the product.
9. When using your winch, it is always a good idea to use as much cable as possible to avoid pulling hard on a full drum of cable. As you pointed out, the full drum is least efficient. If I cannot find an anchor point far enough away I will sometimes use a double sheave pulley just to get more cable of the winch drum while I am pulling.
10. If you are buying cable for your winch consider swaged or double swaged cable. It is well worth the extra cost.
There are quite a few instructional videos on YOUTUBE that are very good.
The self recovery winch on the LMTV is easily capable dragging the truck across flat, dry pavement in a double line configuration. In your scenario, I would suggest finding an anchor point farther away so you are not pulling on the 7th layer of cable. If that is not possible, use pulleys as force multipliers and/or redirects to use more cable for a more efficient pull. If you are trying to pull out your stuck truck you have a 4 to 1 system as you described. So 4 times 6,000lbs is 24,000 lbs minus friction and inefficiency of the system.
Will it get you out? Maybe
Is there a better way of doing it? Yes