When I'm moving from spinning thin to spinning thick, I'll do some pre-drafting down to where I think it needs to be for the thickness, and spin up a sample -- then adjust, repeat, until I can see how thick I need to draft for the spun yarn to come out right. Once I have it right, I save a sample drafted and a sample spun on a card that I keep nearby while I continue spinning.
Also with thicker yarn, less twist is needed for it to be yarn, so put in a little less twist before winding on to your spindle, or treadle slower on your wheel.
A 3-ply will give you a rounder yarn to knit with, but then again you'll have to spin that many more yards before you are done ... if you've time and patience, spin up a 2 ply and a 3 ply and knit up samples to see which you prefer. On the plus side, the singles for the 3-ply will need to be a little finer than those for the 2 ply, so that might be an easier thickness to spin.
(posted by me this day on spindlers)