kz900 biggest tire size.

I have a set of Dunlop Gold Seal K70s on my KZ900 that look new but were made in 2016 (8 yo)... I think I can made some nice mirroir or picture frame with them for my garage...Lol.

I've looked at the available size of Michelin Road Clasic and wonder if there's an advantage or disadvantage to taking a larger size than the original 3.25 x 19 and 4.0 x 18.

 

There is no advantage fitting a wider tyre to the stock rim other than what is recommended.
A wider tyre will increase tyre wall flex and affect the handling for the worse, especially when cornering.

You should be able to go 100/90-19 front, and 120/90-18 rear, both of which are a little wider than stock.  These are common sizes with KZ bikes using the same width rims/wheels.  Of the two, the rear pushes the envelope more than the front.  A 120 is not a big tire per se, but it's max for the rim, if not a little over.  Realize: I've never put these size tires on a KZ900, so hopefully, some others with more specific experience with that bike will chime in.

BTW, I just install these sizes of Road Classics on my KZ750E.  They are a smig smaller than some other tires of the same rated size, so that may help your anxiety.  

Hey Kaw-boy, I run Shinko 230 tour master 100/90-19 front and 120/90-18 rear on my 74 Z1 and they work great. Years ago (1987) I put 120 wide front and 130 wide rear pirelli phantoms on it (thinking bigger is better) and the handling and cornering was noticeably worse, due to the tires being too wide for the 1.85 wide front wheel and the 2.15 wide rear wheel. 

I run 110/90-19 Shinko 230 front and 130/90-16 in the back. Been doing this since 14 and they work great. I had an 18" rear till two years ago then went 16 alloy wheels. This time the rear is tubeless. Solid as a rock and the front doesn't wash out on my dirt roads. The 100 was prone to it and less stable at high speeds.