There's a guy on-here selling Shinko rears inexpensively, and whatever rear you buy, I suggest getting the same manufacturer's
type of tire (rubber compound and ply construction) for the front.
If you do go with the Shinkos, the sizes you're considering are the OEM, and going to a wider front will slow-down the steering a bit. I like the OEM front, you could safely got to a 170 in the rear, if you want a 'meatier' look. The OEM size makes the lazy geometry of the bike steer more-precisely than a wider tire.
That said, I consider the #1 best improvement you can make to a VMax, is to get a 17" or an 18" rear wheel, and running radials f & r. The handling is so-improved, at speeds above let's say, 65 mph, (maybe X2) it's a different bike. While you can run a OEM sized radial tire on the front, a radial tire is recommended for use on a much-wider rim, say a 3-1/2" rim. To get the most benefit out of a set of radial tires, the wheels should fit the recommended size.
It is very-important that you get the same type of tire f & r as you cannot safely mix radials and bias-ply tires. Yes, I-know, there are a few bikes out-there which do exactly this, but they have a team of engineers working on what handling dynamics they're designing into that particular bike. Even in radial tires, there are differences in construction: some tires, the radial plies overlap forming acute angles, while others are at right-angles (called zero-degree) and mixing the two will introduce some scary handling, don't do it!
Also, you want the same type of tire in the compounds used, as on a VMax, if you use the bike's power liberally, a rear of the bike, sport touring tire (or worse, a touring tire) with a sportbike (stickier) front tire will result in the rear tire losing traction before the front. On a wet road surface you could find yourself on the ground before you can do anything about it.
Choose carefully.
Look for the thread about the guy selling the rear Shinkos (link below), he has a really-good price. Compare to this V-rated Bridgetsone (to 149 mph):
Bridgestone Exedra Max Bias Ply Rear Tire | ChapMoto.com at $156.20/ free USA shipping.
(62) Shinko SR777 160/80-15 Rear Tubeless Tires for sale | Yamaha Star V-Max VMAX Motorcycle Discussion Forum (vmaxforum.net)
