I ordered a whole new compressor and pulley thinking I couldn't go wrong this time and would be left with a spare compressor for someone... but the guy at Ebay said it doesn't have a 5.75" pulley. He said I can sort it out with a different belt - is he trying to supply me with an Integra pulley?
You have the correct compressor (Denso 10PA15C), so it must be the wrong clutch, pulley, or both. Of these possibilities, I think it is more likely the clutch itself. The clutch in your picture above sure looks fat. Since your old pulley has been "binned", ideally you will want another 5.75" pulley as well as the clutch.
Regarding your Ebay order, I am not sure which compressor you are getting. It will either be a remanufactured compressor, or if it is a new compressor it is most likely a generic made-in-China (The brand will be "NEW" - it will say so on a sticker right on the side of the compressor - and this is what they mean when they advertise a "Brand New Compressor for Acura NSX 1991-2005" - clever hunh?) compressor that has a clutch with a 5" pulley already mounted. Either way, the reason the guy said he doesn't have a 5.75" pulley is that he doesn't have any compressors assembled specifically for an NSX. These parts are built for volume sales, so they size the pulley for an Integra because then it will fit more cars, hence, more sales. The guy isn't really trying to put one over on you. If you look up the compressor for an NSX, it says Denso 10PA15C, and if you look up a compressor for an Integra, it calls for the same part. They probably don't know about the different pulley sizes. They are just going by the book.
You would have three options with the Ebay compressor if you decide to install it.
The first and best option would be to obtain a 5.75" pulley install it on the new clutch on the new compressor. The pulley
is removable with a puller and can be swapped to the new clutch on the new compressor.
The second option is to keep the 5" pulley and go with a smaller belt. So what is the downside with this option? The 5" pulley will cause the compressor to turn 15% faster, possibly too fast at higher rpms, fast enough to cause bearing premature bearing failure in the clutch. This is why the NSX compressor is "geared down" with a larger pulley - to keep the engine from overdriving the compressor at higher RPMs. I still think this is a viable option nonetheless. I don't really recommend this setup, but I am currently running this same setup without any trouble, so far, and the faster spin rate at lower rpms probably cools the car better. I rarely drive triple digits (I do once in a blue moon...) so I am not personally that concerned about overdriving the compressor, but it is a valid concern. Note that the compressor activates anytime the HVAC system is turned on, even when you run heat or defrost in the winter. (You can manually turn it off from the climate control panel.)
A possible third option would be for you to try to investigate which other Hondas/Acuras possibly do have a 5.75" pulley, and if you can identify one, get them to swap out the pulleys before they ship it. I am not sure if they would be willing to do this, but it couldn't hurt to ask.
I recently had one of these "NEW" compressors installed in my car. My tech elected to keep the 5" pulley, but if I had to do it all over again I would insist that they pull the 5.75" pulley and swap it out. So how is my "NEW" compressor doing so far? So far it is working fine, but I also spend 99% of my time in the lower RPM range, as I am not out hot-shoeing around. I would still recommend swapping out the pulley to one of the correct diameter if you can locate one.