I'll stick my nose in because this sort of thing was within my profession before I retired. Assuming the Mini gearbox has a conventional input shaft the first issue is that the pilot end of the input shaft must
be supported just like it had been by the crankshaft. Gearboxes normally rely on this, that's why they appear somewhat loose when you wiggle the input shaft on the bench.
Then you have to transfer the torque off the keyed motor shaft to the spline without loading the spline unevenly. You rely on the involute teeth under torque for alignment.
A normal clutch disk of course is rattle-loose in the middle so that can happen freely (and cheaply).
A huge problem with a keyway-type coupling half is that the constant back and forth torque can shag out the key if the coupling is "hard", but allowing slight rotational flex will help that, which is what the rubber does, another requirement to add to the list. The clamp style coupling half (as used in the type you've identified) can help or at least delay the issue. But a far better design is what's called a taper-lock hub (see image) where there is a tapered sleeve between the motor shaft and coupling half that is drawn in by screws. These are really effective, far better than what you've chosen.
Generally engineers send the dimensional details of the two sides to the coupling manufacturer with the maximum torque and RPM and they determine the best product for the job. Hacking something together especially involving welding may work for a while but it's not a professional solution unfortunately.
One suitable design would be a rubber-based flexible coupling (see image) with both radial and bending flexibility that is configured with a taper-lock on one side and machined to match the spline on the other, allowing the pilot journal to poke through the center and locate into the end of the motor shaft - with a bushing as needed. Or the pilot support can be part of the motor side coupling half. It's only holding it centered just like a pilot bushing or bearing in a crankshaft. This would allow a radial misalignment error of perhaps 0.001 to 0.003" between the motor and gearbox, entirely practical.
If you want more assistance a useful photo would be of the two physical parts set to the locations you need.
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