The key to swirling is separating out early on. The second key is being ready to go so that if your soap decides it wants to misbehave, you can move at super speed. Here's how I set my kitchen up; you can't see in the deep bowls, but I have my colorants pre-mixed and everything's ready to go.
I soap at close to room temp. I heat my batch of homogenized oils and then let them cool off, lye too. Add you lye to your oils like normal; if your FO behaves, add it after mixing the soap batter a bit. DO NOT USE A STICK BLENDER, just your wire whisk!! Your recipe will trace way too fast. I think people have problems with swirling primarily because they don't know when to separate out. This picture should help; look where the flash of the camera is; there's an oily looking layer; this is the earliest stage of trace, that oily layer is actually the beginnings of soap.
Now start pulling your soap batter out to color. For my mold and the way I like swirls, I do about a ladel full or so; max 2. Put it into your bowls; I hit the bowls with 2 pulses of the SB and then stir about. Rinse off in between colors. Now you're done mixing all your soap batter; hit the base with a few pulses of the SB to make sure it's all good. I do a combination ITP and controlled surface swirl; this ensures that I get color throughout and also get the nice pretty details on the top. ITP swirls are super easy; pour from various heights around your pot then you can either stir once around the pot, or let the movement of the batter do the work. Don't pour all of your batter into the pot, save some for the suface swirl. This is how my soap looks at this point:
Now, you're ready to do a surface swirl. Wait a few minutes until the soap in the mold is at a light-medium trace. You want the soap batter to stay on the top, but if the batter is too thickly traced, you won't be able swirl. You can either just pour the batter onto the top, like shown below, or pipe it on their with anything from a plastic baggie to a mustard bottle. When you pour it on, you get more bold swirls. Piping results in a nice and fine, kinda delicate swirl. This batch I poured.
Now you go to town with your skewer, toothpick, whatever you've chosen. In this particular batch, you can see that the green was a little more thickly traced than I would have liked; it didn't blend as well. I'll also attach a few other pictures; the green and white soap had the batter piped on there hence the finer swirl.
Piping on the mold looks like this:
The bottom line is that you have to separate out early on; I have plenty of time; never had to rush. The other thing is that you need to know how your FO behaves. If it's a dream to soap with, add it to your oils right off the bat; if not, you need to scent each color and the base. Since I figured out when to separate; I've not had a batch rice, seize, or anything. It just takes some practice and patience.