Hey, Doug:
You can use a burning piece of incense, and gradually bring it closer to the sprue-line. Hopefully, the incense smoke is hot enough to tighten the plastic. Too close and it will melt through and curl up. I've had that happen more than once.
Try to get the sprue as tight as possible before you apply heat. That means cutting the sprue as accurately as you can to get it as near the right length as you can. That way the heat doesn't have to tighten it too much. I've found that if I over-do the length too much, the sprue is reluctant to tighten up at all without breaking, melting and curling.
Usually I attach the sprue end to the mast first, then anchor it to the deck or the tie-down point. Sometimes you just have to go with what works most conveniently.
I try to do as much rigging as possible with the sub-assemblies before I attach them to the hull. It makes things easier than trying to maneuver and manipulate the whole completed ship.
Just keep plugging away at it, and take a break when it gets too much. I built a Gloster Gladiator for the Airfix GB years ago--a biplane with lots of rigging. I had to remove all the rigging from the first attempt and do the whole thing over. That was a major lesson in both frustration and patience!
I think using sprue for rigging is more art than science, and it doesn't always go well--but then, what in modeling every does always go well?
USS Missouri in 1945 sounds like a really good choice; and with PE! Another learning curve coming up. As for bending it, I don't have anything except single-edge razor blades, and they usually work pretty well; but you're working in a bigger scale than 1/700. I have given thought to getting a mechanical bender too, especially for rails that might be longer than a razor blade.
But, I've also read that some ship-modelers never apply railing in more than 2 inch lengths; makes them more manageable.
Good luck with Missouri. You are obtaining some great results!