135/70R16" or 15" rear tyre on a XJ900R?

I have a 1983 XJ900R with a sidecar. It has a leading link front end with a Avon triple duty front tyre (flat profile like a car tyre) and a steering damper. The rig rides really well at all speeds except that the rear tyre is a little slipery. The rear tyre is currently a 4.50x18 Avon old style flat'ish tyre. I would like to fit a 135 car tyre on the rear to give me some more grip. The 135 tyre will just fit next to the drive shaft. Just need a replacement wheel assembly that will take either a 16"x3" or a 15"x3" rear wheel of another model Yamaha (prefer disc brake so I do not need to change the rear brake setup). The 135/70R15 & 16 seem to be the only sizes available that will fit the width. Any suggestions?
Thanks. Mark.

Ok, this query was a few years ago, but this might help someone.
Just looking into this one myself.
I'm figuring out if there's enough room to fit a 15" V-Max early wheel (hub might be too wide) because it being a cast wheel with disc, and I have a 135r15 Nankang ready to go on it. Failing that, I would think the XS1100 16" would be a go-er.
As far as I can see, the other options are nearly all drum-braked cast wheels (Maxim, etc) or spoked with drum (XV750, 1100 etc), which are not my preferred way to go.