Need to rent carpark space for reno work

So just pay it ... it's an extra $700 in a renovation that's undoubtedly many multiples of that, and you're doing it once. It's not worth your time and energy to fight it. You'll get worry lines.

the scaffolding is for us to set up the external venting hood. How much does that add to the price of an apartment (vs internally circulating hood)?

buy less shoes...

Some people value its function, some value its look, some don't care, some don't cook. Unfortunately, the norm in New York for standard-grade ranges/cooktops is unvented, so it'll probably never be a deal-breaker.

save some money, rip out the kitchen and plaster the entire wall with take out menus... you are welcome.

Our building has gone through this periodically over the years for maintenance, Local Law 11 inspections/repairs, etc. We have paid the adjacent parking lot for the use of its space. It may be too late now, but you would have been better off just asking the attendants, as they probably would have calculated that quite differently (i.e., five spots for you, five spots for me). Although the lot usually just provides a price and typically applies a small discount rather than a multiple of the spaces, I suspect that erecting and dismantling the scaffolding will take up much more than the space occupied by the scaffolding.

Don't know how high up you are going, but if it is only a couple of floors it may be a lot cheaper to get a bucket truck or scissor lift rather than installing scaffolding.

I've already put in calls to the Food Network trying to pitch "Cooking with W67thstreet"...plaster the walls with take out menus, my kind of kitchen!

I should add that we pay based on what the lot owners say is their daily revenue per space, which for different days/times of the year is significantly more than the posted daily rate because the minimum charge is more than 1/2 the daily rate and space may turn over several times throughout the day. It is possible that 3x the daily rate is not unreasonable depending upon how active the lot is.