If it was me, I would not finish them at all, then the heat will bring out the smell of the wood. If the wood is fairly plain, I would go for a dilute cut to bring out the grain, and leave it at that. Would probably be worth doing a prototype first, just to see how they will react though. Also worth understanding if these are going to be a single holiday season use sort of thing, or if they are expected to last for years under regular abuse. If they are single holiday, then I wouldn’t worry too much, and just get the chips flying, enjoy dinner, then use the mats as firewood.
Colin, Czech Rep.