It seems to me that DOT and TLC are caught in a catch 22 here. Yellow cabs don't serve the needs of local residents because they do not make enough money off the short trips to justify their expenses etc. By and large they serve Manhattan simply because volume is higher and the likely hood of a worth while trip is higher too. Yellow Cab owners pay a hefty price for their medallions which allow them to pick up and discharge passengers anywhere in the city they want legally. This is technically an exclusive right granted to them, keeping the competition down. Since the city grants this right to medallion holders, it can't create a space that legitimizes a practice this is technically illegal and cuts in to the right granted yellow cabs by virtue of the medallion they pay for.
Even making an official exception for areas like ours that are under-served by medallion cars sets a precedent for other areas all over the city that would cut sharply in to the medallion cab privilege.
So the currently "solution" is to simply not enforce the current laws allowing for gypsy cabs to pick people up in "outer - borough" (I HATE that term) areas like JH etc. But enforcing that law every now and then when the volume of gypsy cabs in a given area gets too high.
Once upon a time, there used to be a Taxi stand on the north east corner of Broadway and 75th St. where there is now a bus stop (I believe it's the Q53). If you look closely at the ground you can still see the yellow "Taxi Stand" words there. I recall getting a yellow cab there once a long time ago to take me to JFK.
Perhaps, a taxi stand could be re-created for yellow cabs, and the culture of non-enforcement could allow for gypsy cabs to line up there rather than cruise around. This might also make it easier for TLC to spot check drivers and make sure they are on the up and up.
Alternatively, an enterprising car company could open up in one of the empty MTA venues and provide radio car service, so one could walk in and request a car on the spot, which would avoid breaking the law all together.