I use the washer and dryer on gentle. Depending on what it is I sometimes put the garment in a lingerie bag to keep it from getting beat up. I've never had a problem.
As for cables.. yes, blocking can help them, but since the yarn is primarily acrylic blocking won't keep the shape as well as more mostly wool would. You most likely would have to block it every time.
Like, for scarves, they always fold inwards on the sides, even when I do a seed stitch border & slipping the first stitch in each row. Scarves & fair isle patterns really need the blocking, IMO.
Unfortunately this is the nature of the beast. Stockinette rolls if you don't do any border and tends to fold in along the border when you do. If it's ALL wool you may be able to get it flatter, but even then it's tough sometimes. You just need to learn to love it foibles and all.
I always buy Wool Ease yarn because it's semi-affordable & feels nice against the skin. I'm about to start a project with the Thick & Quick yarn you mentioned, too. That blocks well? When you do your wet block, do you use soap or just water? I've read people doing both.
Nothing wrong with Wool-Ease, I just prefer Encore myself. Thick and Quick won't block any better since it's basically the same thing as Wool Ease.
I use a hand wash if I'm going to block something. Soak or Eucalan are my favorite and you need very little and they don't require rinsing.
Now... all this being said here is a site that says you CAN block acrylic and have it stay if you steam it. Just be careful when you do it so you don't kill the acrylic. I probably wouldn't use this for a hat, but I want to with the next baby garment just to see how it works.