gravelstudios as a person with a degree in music education, the bassoon is imo the hardest instrument. (at very least, it's tied with french horn, but I'm a brass player primarily, so I at least had some frame of reference with fh. a woodwind player's mileage may vary).
Old_Zircon As double reed instruments go I'm pretty sure the duduk is harder. And then there are those weird quadruple reed instruments you find all over from north Africa to southeast Asia where they're basically like laying a bassoon with much stiffer reeds that are layered two reeds per side. I've never tried one but by all accounts they're about as difficult to lay as anything you're going to find.
As far as unsynthesizability, last I checked nobody had done a convincing physically modeled tabla either (the tabla being pretty much the gold standard for complexity when it comes to membranophones).