You Bet Drunkenness Rules!!!
Oh that was a question and not a statement. oops! Treating it like a poison might work. Would explain dwarves need large quantities of ale. Make the DC based on the proof and quantity drank, 1 beer is DC 10, double shot of tequila could be a 15 or so, Jagermeister a 13, except for me then it is a 8

. I am not good at assigning DCs so you might want to take more time on it. Make the effects cumulative like each drink adds +1 to the next DC, or +2 if you failed the previous the save. As for the poison dmg, primary could be -1d2 Wisdom, secondary -1d4 Dex or something. I'll do some research tonight with some Guiness and/or Jagermeister and get back to you with better DCs and dmg numbers.
As for the having the player drink, good idea in theory, but alas we have a no drinking rule in my group. It is annoying too, cause the on person who refuses to drink in real life insists on playing his dwarf as an alcoholic.