You still haven't told us how you plan on using the slings.
Holding a block for catching a load: Big tenex is fine, or maybe smaller double-braid rope, double tied if you prefer. The real load is taken by the bull rope. If you have a stretchy bull rope and it is running up to the block and then back down to a friction device, you may have 40-80 feet of rope that can elongate. At that point, the elongation built into the sling becomes unimportant, because the shock load is being absorbed more by the bull rope.
Run a steel cable for a bull rope (or amsteel), and you will get more shock loading on the sling.
Eye Slings for rigging to a crane lift: I would feel perfectly comfortable with 3/8" amsteel. At almost 20k breaking strength, you certainly have a huge working load with a doubled up sling. That 3/8 amsteel is pretty light on a climbers belt, and nobody with any sense will be shock loading the crane.
Light slings for attaching to speedlines: almost anything with sufficient strength will do, because the speedline will be absorbing most of the shock. They have a built in "let it run" ability not found in most rigging.
I would say that any rigging sling for heavy drops on a block should be twice as strong as the bull rope. That, or doubled up to produce the same effect.