Yeah, they are great machines. Easy to work on, and a good following of folks who are willing to help. They are pretty bullet proof, with a few weak points being the BGB, axle tube, and steering components (steering gear, ball joints, and center pivot on the front axle)
I like the way they handle and the old Briggs' are a great, long lasting engine. It's amazing how these will do so much more than a modern lawn or garden tractor. My passion for them started with the dream of owning some of the rarer attachments...there are so, so many, both common and rare. The attachments are built like the tractors and are easy to use and work well. At some point I will try to document how many I have. It's a lot. Many 'dream come true' moments. =]
I don't know of a modern equivalent to the Schenuit. Best odds are to find an old 6-12 set of rims with the tires in OK shape and tube them. I don't believe the B-10 ever had 6-12's, but some early one's were said to wear 8", with their later cousins having 8.5" Goodyears. I'm not sure what 6-12's the B-1 wore...Goodyear Terra's as well?
We need to see a bit more of your machine!