Unfortunately, I have those same "hard" cheese questions! It's why I've hesitated in making them, too. Have you checked into Ricki Carroll's (the Cheese Queen) book? I don' t have a copy yet, but I understand she covers hard cheeses in it. Good luck!
Ahhhh, I make aged and hard cheese and the solution for me to the "cave" is a wine fridge! You can get different sizes (6 bottle fridge for small batches, 2 case for your wine and cheese!) set it at 55 degrees which is good for both coexisting delights (cheese and wine) and I create humidity by placing a damp towel in the fridge. It has worked great.
I made a cheese press. Boards and long screw things. I place paint or large soy milk containers to get the desired pressure. Primitive, yes. Cheap, yes. Works, definitely!
BTW, the kitchen fridge does not work! Don't even try it!
OK, I'll just throw in another 2c here, I heard there's a way of making a natural refridgerator with two clay vessels and water, one inside the other, and it was used to create natural refrigeration in Africa, so it should be cool enough for the US. If you want to do something that doesn't require electricity. You probably need to replace the water frequently though, which is not as eco-friendly in NYC--but if you can then use that water for something like handwashing your clothing or irrigating plants or something that might make it better. The cool-ness doesn't come from the water itself but from the convection currents or soemething.
Also, ants build their hills (big, 3-foot high) in such a way that the convention currents cool them too--scientists don't know how they work, someone told me, but I saw the thing itself, and it's amazing they were able to build something 3 feet high and only about 9 inches in diameter, so I can easily believe that it also was self-cooling.
The other answer could be geo-cooling--the earth is always 55 degrees, summer or winter, so if you can conduct heat down from your cheese into the earth somehow then you have it. Plug into the grounding prong of your socket? (would that conduct enough heat?) Not really a complete answer, but I'd love if anyone has any insights to keep the converation going.
And the offer of a basement in Yonkers is still good! you all mkae my mouth water!