Even though I havent made one, I did get 4 Strands of Rawhide for christmas and have watched it about 100 times since. I have also seen a few people braiding them on tv. On the dvd, Randy cut the string larger than 1/4" and depending on where he cut it (belly vs back) he would make it a little wider at the stretchy parts. For the areas that are fairly firm like the back, I would cut it at probably 3/8" and along the belly maybe 1/2". That way when you stretch it, you still have some to bevel. You may want to do a few practice pieces a few feet long to see how much stretch you are able to take out and how much smaller the strings get. As far as cutting a wider strip to try and get two, I wouldnt do that. The wider the initial cut on the string is, the harder it is to get the stretch out of the outside edge of the string (and the curvature from cutting it off a circle) to get it into a straight piece.
I dont think I would use a rounder until after the whole riata was finished because if your riata is say 1/8" in diameter, you would need to use the hole size thats slightly smaller so that it holds the riata tight enough for you to actually pull hard at each plait. This would cause your braid to be compressed at every point the rounder held the riata more so than the other areas. I would use a vice with canvas or leather on each face to protect the strands, but a wider face thats holding the riata will be better because it spreads out the force over a larger surface area. Randy also said that if you break a strand and have to splice a section in, you shouldnt pull it through a rounder (or at least stop before you get to the splice) because the splice will be slightly larger than the other areas.
What you could do is get a good clean 5 gallon bucket and put the finished section in there and as you braid and move it through the vice, just coil it into the bucket.
Hope this helps,
CW