Back in student or just post student days a mate of mine got an old Jawa 350 with a side car, that is the only combination I have ever ridden and I refuse to ride another to this day. I have no problem riding in the chair and have done many miles both being pulled by the Jawa and later when I welded the Jawa's mounts to an unlucky Yamaha XJ650 with a Migmate 100. The XJ and chair did many rally seasons often pulling a trailer, I did not know any better in those days and nothing ever failed but I don't think I would do it again.Sidecars have a habit of twisting the frame too, something you'd want to check.
I've often thought that about the BSA M21, I ride a M20 which is the 500cc version rather than the 600c single cylinder side valve of the M21 and it's defiantly not a speed machine, even with lower gearing and 100cc's more grunt/longer stroke I'd imagine it's pretty darn slow.A 350 two stroke pulling a sidecar can not have been exactly a speed machine.