Yeah, exactly! Perpendicular to the limb crosswise. You can rubber band them in place temporarily if they stick out on the sides, or run string through the center and around to tie them in place.
Remember, the cable will stretch at first, so make your cable so it "braces" the bow, oh, say 2" in the wrong direction. Then force the tips down to stretch it. Even better, tie the string on with less brace height, then start binding it down against the limbs incrementally. Like tie it down over a 1/2" dia strut at the handle, then tie it down midway out each limb. The reflex will increase. Then stretch it. You can keep doing this, and twisting like a bowstring, until you find the correct length. Then you play with the struts. Put a couple here, and there, and bend it on the tillering tree a few inches with a longstring, just like you would any bow. You can brace it at like, 2", and move the struts around, add and take em away, and mess with their diameter until you get what you want for tiller.
Then, if you wanna be fancy, rebuild the whole thing with pretty wood struts the right size. Or trim your bamboo to save the weight, a tie the struts in place to the bow permanent tly, and again on the front if you want to tie the cable down (I always have, just because t's that way on the Inuit bows I looked at).
As far as the cable thickness, I can't tell you exactly. The position/geometry of the cable and bow actually provide fairly short stretch, but you have a lot of leverage to do it. The cables always ended up thicker than the bowstring, for sure. And I always used nylon artificial sinew, so I don't know how Dacron will act. I'd start thicker than you think you need, and cut a strand or two out if you need to. Also, thicker cable can be closer to the back of the bow, or thinner one, lifted higher on struts and still equal the same draw weight.