This doesn't meet all of your requirements, but I would ask you to reconsider the need for people to be fooled about the number of floors. Rather, we can hide in plain sight by fooling people about the layout and contents of those floors:
1. For example, a huge luxury hotel with amazing luxury suites on the top three floors. Several different reclusive billionaires end up renting all of the suites on the top floor on a pretty-much permanent basis. You need to use a guest card to take the elevator to the top floors. HQ goes there. The recluses of course need their minions, who show up every day...
2. You could also do this with penthouses in a very exclusive condo building. In both cases, the floor isn't hidden, it's broken up into units in such a way that people don't think about it as a large office area.
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If you insist that the floors be "hidden", I'd think you could still take the top N floors and build a conference center, theme park, or some kind of area that would have a large auditorium in it. There would be "fake windows" to keep the look of the outside even though the Auditorium is a black box with no windows. "Looking at the top floors, you can't even tell that there's a huge no-windows auditorium up there. The architects cleverly placed fake windows in the same pattern as windows below." A "four-story-tall" black box auditorium will be extremely hard to see in perspective. It could easily be three stories tall with fake catwalks, ducting, etc, and since it's all dark up there -- painted black actually -- with lights shining down to blind you, who would know there's an entire office floor up there?
4. Or have the top two floors be HVAC and surrounded with huge LED video displays that play ads, etc. What looks like a solid panel of LEDs from the street would actually just look like a grid from inside, and the brightness of the LEDs would keep people from having a clear view behind the lights. Have a super-efficient HVAC system that only occupies the core of those floors -- which you would immediately see if you managed to get to that floor on the elevators -- and the periphery, with it's nice view, would be yours.
In the last two cases, people would know that the floors are there in some sense, but you'd fool them as to the contents and from the inside it would be very difficult to tell any different. In addition, it would provide the excuse for a variety of different people showing up.
And ultimately, what better place to hide a super-secret HQ than in the brightest and most visible spot in the city? Hide in plain sight. 89