In case this happens in the future, I would offer one alternative path that might work if you happen to use Uber/Lyft at other times: simply ask the driver if they would be interested in working at that specific time to take the ride. Unless Manhattan has increased vastly in population since I last lived there, anyone doing that sort of service is going to be known or at least familiar to at least a quarter of the population, which means that they're less likely to say "yes" and then flake on you because they know word will get around to people who's opinions they care about.
You're not even violating the spirit (I can't speak to the letter) of the ride service agreement, since you're not asking for work outside that agreement, only if they'd be willing to ensure that they're available at the relevant point in time.
As a side note for others: this is a small airport. The notion of having "a line" to get through security is almost laughable; pretty much everything flying out of it has a seat count in the low double-digits, at most. Before 9/11 pilots regularly flew with the cabin door open so that they could chat with the passengers. While you could land something like a 737 there in a pinch, you wouldn't want to, and I'm not at all sure the runway is long enough to allow take-off afterwards. Ride service from the hotel (singular then, probably still) is "they wake up their driver and have him take you there in the one shuttle bus they have."