It would be the surface area, not the mass. The copper is only a carrier, it's the paste which does the work.
Smelting pennies sounds way too difficult. 3mm would be ok and very stable but a bit harder to work with. I would prefer 1mm and supported with plenty of standoff spacers on both edges. Silver would be a good (expensive) option, if you could find the right supplier. Here is a supplier of pure copper strips in all sizes, For a box the same size as mine (300 x 280 x 90mm), I suggest you buy copper strips 50mm wide x 1mm thick x 1000mm long. Then cut the length to suit the box. Just click the squares that match the sizes to get the price and availability.
If you wanted 2 or 3 layers, you would need 2000 mm long. 1000mm would be sufficient for a single layer.
https://www.amazon.com/Bopaodao-Copper-1000mm-99-99-Crafting/dp/B09N2FLRD9/ref=sr_1_264?crid=1ABC39DTT54TU&keywords=copper+strips&qid=1649107325&sprefix=copper+strips+,aps,631&sr=8-264&th=1