I havent done a project where it requires switching needles like that before, but it would make more sense to me to just slip the stitches from the small ones to the bigger ones. What did you originally do? hope this helps!
This is something you encounter frequently when you do a sweater with ribbing on the bottom. You knit the ribbing with a smaller needle to make it firmer and stretchier. Then you switch to a larger needle for the rest of the sweater. (Your gauge swatch is usually done with the larger needle and the stitch pattern of the whole sweater.)
Why go to the trouble of slipping the stitches to a larger needle, then knitting? Just knit them off with the larger needle.
(Besides, it's durn hard to shove small stitches onto a large needle.)