Matt--Installing a tii engine in a non-tii is not that hard. Different throttle linkage, add an electric fuel pump, route high pressure fuel through metal line under car and return through the plastic line. Purchase a warm-up relay or and add a wiring harness for the cold start solenoid, or just do a push button as has been discussed here. The KF pumps are robust (mine did well over 300K miles without ever being touched) and linkage setup is simple once you understand it. Buying an engine whole as you suggest instead of piecing it together from parts is more cost-effective. Also, the standard 2002 block does not have the KF oil return pipe, though it could be added. Upside is 130 HP stock compared to 100 HP stock 2002. Downside is that you can't modify much past 150 HP without getting into some $$ due to limitations of the stock KF pump. I'll certainly agree that modern EFI gives you more options and better fuel/spark control, but a tii engine set up properly is a very nice engine.
Cost: Depends on if you are looking for "brand new", freshly rebuilt, somewhat used or very used. I would suggest setting your budget and expectations and then seeing if there is something available that meets your price point. Not a quantitative answer, but saying somewhere in the range from free to to just shy of $6K-$10K (if you could find a factory NOS complete engine) is not that helpful either. The "heart" of the tii engine is the KF fuel pump, which costs $700-$1000 to rebuilt, plus the cost of a core. Add the mechanical injectors (which even used are not cheap), a throttle body in good condition, the intake plenum and manifold and the tii front cover and you will see there is quite a bit of cost involved in a tii engine beyond the basic M10 head/block that any 2002 engine will require. At some point, depending on your budget and if you prefer to play with mechanical (old school) or electronics, considering modern EFI makes sense. If I went electronic I would do individual throttle bodies (ITB). I have such a project under way, but it is taking a while to complete.
Source: Again, depends on what you want. Ranges from junkyard to parts car to 2002FAQ/E-bay to contact a BMW 2002 specialist engine builder.
Are you still doing the M20 turbo project as well? Best of luck--Fred