Awesome work, quinty!
For technical aspect on any new 1M, I'd rather see a turbo-4 (petrol) than the high-revving straight-6. Especially if that I-6 is the steel-blocked version from the previous M3. Aside from cost, there are weight-savings issues. BMW's turbodiesel 4's are what, about 160kg? Compare that with ~217kg for the old M3 engine and 190kg for the N54. With magnesium-alloy block, and 2 fewer shorter cylinders, this could result in rearward weight bias that Ferrari have acheived to excellent effect in the 612 and 599. An LSD would help even further (and more importantly allow better power transfer to slipping wheels). And please, no runflats. At the very least, optional R-compound tires.
Cost-effectiveness:
This pretty much rules out extensive use of carbon fiber. But how about more use of thermoplastics, like on the E92 and E60/E63 front fenders, assuming the 1er currently doesn't have it? Maybe lightweight plastic hood with aluminum skeleton (if legal). All of this helps to move weight toward the back.
Fewer standard features: just a basic HVAC system (doesn't need to be dual-zone & automatic), no heated mirrors, 4- or 5-speaker stereo instead of 10, and cloth interior for the US (and deletion of cornering lights, retracting headlight washers, etc). Some of this savings in equipment cost will offset the application of lightweight technologies.
Another sticking point is the styling: Aside from the seemingly high price of the 1 Series coupe, people often say the sagging lower beltline and/or wide-eyed stare is the final deal-killer. This is an easy fix, that makes the price considerably more palatable for some.
I've read some comments on various US-based forums and sites, and there does seem to be some demand for the hatch. Some here think the hatch is even better-looking than the coupe!
And how about some more special color options. BMW could take some pages from their own past (2002 and E46 M3).
Oh well, I don't see this working in the States. Such a car would likely start around the mid-40K level. People would then say it's bad value because they could buy a 528i/GS350/M45 or loaded Lexus ES or whatever at that price. But if you made it very exclusive like the E30 M3 or E46 CSL, it might work.