Would it be possible and cost effective to swap out the 2003-05 Automatic CVT Trans with 2006+ Trans...

Came to ask the guru's from across the pond...

^^^...first MINI and first thread.^^^:D

I'm sure with enough money and expertise, you can do it. The computer controls a CVT in an entirely different way than an "normal" automatic. Aside from mounting hardware adaptations, you'd need to control the newer automatic with a different ECU. A manual swap has been done and it wasn't entirely easy or cheap.
Possible? Maybe................ probably.
Cost effective? How big a bank account do you have? While you might consider something reasonable, I might consider it outrageous. I have a CVT which, for the time being, is working flawlessly. If it breaks, would I consider what you're asking? Most likely not. For what it would cost to transplant a newer auto or even a manual, I could probably just go and buy a factory overhauled one. And for that kind of money, I'd probably try to find a salvage unit or throw the car away. My first choice would be to sell it while it's still working, just in case.