Here's a wacky idea.
If folks were able to get a 150/90-15 to fit, which is nominally 5.9" wide and 25.6" in diameter, then an old timey, 5.00-15, which is 5.1" wide and 24.4" diameter should fit on your LS650 easy as pie.
https://lucasclassictires.com/tires/500-15-bf-goodrich-2-whitewall/And, the listing says that it's designed for a 3" wide rim, so fitting on the Suzuki 2.75" rim isn't much of a stretch. ( I'd verify this spec. with the manufacturer)
The icing on the cake is that car tires are known to give crazy long tread life. This might be the last tire you ever need to buy, and more economical in the long run than even a Shinko.
Is it considered "going darkside", when it's a WIDE whitewall?