I have an 11x14 that works tolerably well.
The key to contact printing is the psi [pounds per square inch/pressure]. 16x20 is 320 sq inches - to apply a pressure of 1/2 psi (a not-too-well filled party balloon's worth - about what most frames can manage) you would need 160 pounds of clamping force.
You only need one sheet of glass. You can make the backing from 3/4" plywood. You will need to cover the plywood with thick felt. A frame around the glass will help to distribute the pressure from the clamps.
Large contacting frames use vacuum to clamp. One side of the frame is glass, the other has a rubber blanket attached to it. Air is evacuated and the blanket clamps the artwork to the glass with atmospheric pressure - 14 psi. A 16x20 frame would have over 2 >tons< of total clamping force. With the rubber blanket there is no net force on the glass. There are contacting schemes that use a box with holes as the evacuated side and a thin sheet of plastic that goes over the artwork to allow evacuation of the space between the a/w and the film.
You used to be able to get contacting frames for free as print shops were converting to digital and 'laser plates' right and left. You can find them on ebay - the larger ones cost much less than the smaller ones. And they weigh a ton [almost literally for the large 40x48" ones]. Search for "vacuum frames" and "exposure units".