First, a few caveats:
1) I have a TDI for sale on the board as we speak.
2) While I am a Mechanical Engineer, I have not actually attempted what you speak of, but I have thought about it.
As far as I can tell, the biggest issues revolve around everything else, not the actual engine-to-engine swap. As you rightfully spot, the cars are designed to physically accommodate the parts. The issues come in the unknowns (at least, unknown to me - clearly they are knowable) - The multiple Computers and controllers that are TDI centric (not just engine controls, but all the other bells and whistles with the car) and whether or not they have all of the addresses to handle a non TDI body/wiring setup. You would like to think that it is pretty standard stuff, but I've seen to much to know better...
The fuel tank/pump/line are items you probably just want to replace outright as well. I also admit to not knowing whether there are flavors of gearbox out there - I do not know if all of the manuals in a given model year are alike across the engines released in the US (I'm only allowed to play with automatics, though with the advent of DSG, that's not so bad anymore).
I would surmise that the level of labor involved may outweigh the cost of parts, even if you do all of the work yourself (never forget opportunity cost). That's not to say it can't be done, because clearly it has.