Just noticed a little leakage from mine after last fill up.  Honda part on order.  Thanks for the info.

So.. to recap (huh huh)  

The Honda and Suzuki gaskets are about the same thickness.  Replacing with the Honda gasket can fix it temporarily, just by virtue of being a fresh gasket, but probably not much better than a new stock gasket.  

Rotating or flipping the stock gasket fixes the leak on some caps, but again, probably not for good.  I imagine it will eventually pack down and get loose again.

The spud washer is thicker than stock, but not always made of a gas-resistant rubber, so you have to treat it with gasket dressing to be sure it won't swell or dissolve on you.

The best options seem to do that (use a spud washer and treat it) or shim up the Honda or Suzuki gasket somehow.

I tried to use the Honda gasket fix, but the gasket deformed two days after. I order an OEM gas cap and now is fixed.

Just wanted to add in case it could help someone.  I was having the leaking gas cap problem and added a shim as suggested but the leak continued.  Since the plastic cap that houses the catches sits on top of the rubber ring I am not sure how a shim behind it makes it seal tighter other than just adding bulk.  
I sanded the bottom of the cap where it contacts the gasket with sandpaper on a flat surface which makes  the catch closer to the gasket for a tighter seal.  It worked well and did not interfere with the operation of the catches.