Okay, I'd gone to a bunch of hardware stores looking for hollow-braided mason's twine. Twisted this, solid-braided that, not strong enough, just a total pain in the *** and couldn't find what I wanted.
Once again, Walmart had exactly what I was looking for. It's in the fishing section, and it's called Lehigh Catfish Dropline #18. $5 for 240 feet. 100lb tensile strength. Other manufacturers call it catfish trotline.
It's super strong, no noticeable stretch, and spliceable!!!! To demonstrate, I attached a tiny whoopie sling I made out of it. I'll use this stuff for pretty much everything other than suspension lines.