best rope for splicing spider leg balancers??

And depending on the loads you anticipate, you might consider something that is a little more resilient like something with a tighter cover (sorta like ultratech has) or maybe you could even use icetail if you wanted to stick with single braid.
We've used tenex with great success but it snags and puffs a lot.

We're experimenting now using double braid slings of a suitable length and are likikng it a whole lot more.

Because they are less likely to snag it makes tying them to the load a lot eaiser.