The Minor, AFAIK did not have a separate chassis, it had monocoque construction.
The engine was a BMC A-series, so one from a Sprite would be OK (single carb though), but I think the gearbox is different. Front suspension is also different - the Minor had torsion bars. MGBs had a B-series engine and Triumph used their own engines, so neither of those are suitable.
That said, although I am British, I actually know more about American cars from that era, so I'm sure someone else will chime in with more useful information.