Consumption bar with a cap

So getting an “open bar” at our venue is extremely excessive ($20 per person PER HOUR) so there is no way we are paying that amount because we won’t get our money’s worth at all.
Our venue organizer recommended doing a consumption bar, so our guests don’t have to pay anything, and FH and I will (at the end) just pay per drink that was ordered. My only concern is, each drink is $10 (venue is definitely overcharging, but it is what it is) and we are having 100 guests, so if everyone has 2 drinks, that already comes out to $2000, not even including tax and tip! Our planner then recommended that we do a “consumption bar with a cap” so when and if the bar tab hits $2000, it becomes a cash bar.
We are having a lunchtime reception and many of our guests are not drinkers at all, but we do have a decent amount of people who do drink, and probably a few who will drink heavily. But i can’t be sure of this... it is possible we won’t even come close to the $2000 limit, but it’s also possible that one of FH’s old fraternity brothers will have 10 drinks before the cap is hit, and then my great uncle will want a drink later and will have to pay for it himself since the cap has been hit, which doesn’t seem fair at all!

So my question is this... is there an eloquent way to ask people (I was thinking maybe a sign, or even just saying something) politely to please have 2 drinks on us, but that if they want more than 2 to pay for it themselves so that it’s fair to the other guests? I don’t know how to do this without seeming stingy...