In your intro to the item about the Kawasaki Tengai you mentioned featuring other big singles in the future. If you are interested I have an Aprilia Moto 6.5 1996 that I have owned since 1999 that you would be welcome to ride once it is back on the road, probably around July. Much fun was poked at these at the time but to me it was simply a big single roadster and I could not quite understand why the almost universal mockery. But my skin is thick: if you rode it and you too thought it was daft I would not mind in the least. It would still, to me, be a solid big single with the reliable Rotax motor. It is not pristine at all and has all the appearance of a 22-year-old bike which may make it unsuitable for your purposes.
...to an acquired taste!