I have searched and confirmed the 19" 370 Rays wheels fit. Has anyone mounted 15-16 Enthusiast wheels on a 350?

 

The Z34 uses a different lug seat design than our Z33s. You'll need a complete set of Z34 lug nuts to mount those '15-16 Rays.

 

^^^ Totally this. Shank lugs vs conical.

Also, the Z34 wheels have relatively high offsets so you'll need to run spacers to make them fit correctly on Z33. And, if they come with tires, they'll be the wrong size. If you can get them without tires, you're better off picking the right size tires of your choosing and not paying for the Z34 tires which will be too tall.