I would definitely pick this option. Jut as your partner didn't know they were standing on a body of water, you don't know where the water body begins or ends. Being on your belly helps spread the weight instead of focusing it on one point and risking breaking the ice and falling into the water yourself.
Having taken them out of the water, I'd get us back to the fire, get naked (because their clothes are completely wet, possibly frozen, and I just got on my belly on snow, so mine must be damp as well), get under the thermal blanket I think we have and simply sharing body heat by the fire until our clothes are dry (thanks again, fire) and we may proceed.
Yay for flammable tortilla chips ;)