There are lots of options for what to do next. Usually, the option that is both simplest and logical is the best with these plants. I would just plant the plugs in their final home, and keep a vented transparent cover them for a few days. Actually, my seeds are sprouted right in their coco filled pots in the tent.
All these multi-stage seed manipulations - soaking seeds, removing seeds and putting them in plugs or paper towels, transplanting sprouted seeds to paper towels, and transpalnting plugs and sprouted seeds from paper towels - just seems unneeded (if not crazy) and not suited for sensitive autos. Seeds should not have any problems sprouting and getting a good start in whatever media/soil you are using, in their final home.