You could try drinking a good bit of water beforehand – not so much that you get sick before the contest even begins – but enough to dilute the effects of the alcohol.
Remember that booze dehydrates you, and the best cure/preventative for a hangover (for me & many others) is water.
Also try consuming some pasta or bread just to line your gut with something “spongy” for absorption purposes. You should know that liquor on an empty tank leads to a faster shit-faced state.
Now, the food & booze strategy is a given.
And I have successfully used the water / re-hydration technique to stop the room from spinning wildly while laying in bed – which is usually the precursor to me getting sick shortly thereafter – on the few occasions where I’ve had too much to drink.
But, I’ve never tried any of this in the context of a drinking contest, so don’t come yelling at me if you try it and it doesn’t work.
I still think your best option is to not go through with this contest at all.