I am the Kat that Walks By Itself

My method was to take the frozen batter out of the ice cream maker, put it in a tub, and add the swirl stuff at that stage. With a wider tub you can put the frozen batter in all at once. If it's a deeper tub, put in some batter then blob in some swirl. Drag a knife through to make patterns. I did some really good dulce de leche like that.