The no small MINI for the US situation is just what I know right now. It could change.
Canada won't help because it shares models with the US (same crash standards).
I don't know what's happening inside the factories but your questions are presupposing that Oxford is not doing anything but making the F5x cars, and that retooling for a new model requires a serious disruption in the current series production. Both assumptions could be false. Consider that BMW...
A few corrections and additions to the Motoring File reporting:
J01 will be made in two versions, E (175hp) and SE (215hp).
Production starts at Oxford in November 2023.
China production will begin a few months later.
No US version of J01 exists yet.
Aceman production code is J05, not J02...