The degree of separation in the 3.8L is wider. Meaning that the engine is wider between the valve covers. The 2.8L is a 60 degree V6 while the 3.8L is a 90 degree. However that being said the 302 Windsor V8 is also a 90 degree engine. I am not sure what the deck height difference is between the 3.8L and the 5.0L, but going to a junkyard and taking some measurements would be first on my list. I own a 2.8L version of the Ford Pinto, and can tell you that the engine is a fairly tight fit on the passenger side, as the battery mounts on top of the pass. fender towards the back. Also the clearance between the exhaust manifold (pass. side) and the fender is maybe 1.5". On the Driver side the exhaust clearance to the fender is about the same. You also may run into clearance issues with the steering system. So just like with a 5.0 install, there will need to be some clearanceing. I think it would be doable, but there will also be issues with wiring according to what year of 3.8L you get. The 3.8L has a different ignition system, whereas you can use a duraspark setup with the 5.0 I am not sure if this is an option with the 3.8L (maybe someone else can pipe in here). So as with any "unnatural" swap there will be more to it than it looks. The expense of the whole install would be at least as much as a 5.0L if not a little more. You will need to determine for yourself if that is worth it to you.
As far as an overdrive tranny goes? I would think that since you maybe putting in a 3.8L you wouldn't really care what tranny you use, so I am going to through an idea out there for you. How about using the Chevrolet 700R4? it is a proven tranny, and advance adapters makes kits to mount ford engines to it. I am sure they make one that would work for you, but you would need to ask them. This tranny is a purely hydraulic transmission that is stand alone, so no computer.
Of course another idea to toss around (Hope I don't get booted for this

) is the Buick 3.8L + 700r4 swap. The Ford 3.8L is rumored to be a very similar copy of the Buick 3.8L V6 (Buick had it first). The main difference between these engines is that Ford used aluminum heads whereas Buick used Iron. Of course there are bolt pattern differences, but that would not really matter if you were going to use the 700R4 tranny. If the engine could be physically mounted in the car, it would be a pretty strong combo and fairly reliable. In fact you could use the HEI ignition system or even a distributor-less system if you wanted. But this is purely blasphemous banter on my part

If I were to ever do a swap I would be putting in a simple 302 backed by a 700r4. The duraspark powered 302 is not only simple but there is a huge amount of aftermarket support. Plus you get the experience all of these guys have with putting one in. Advance adapters makes a decently priced 302 to 700r4 tranny adapter that is super easy to install. Also you get the economy that the 700r4 gives with its overdrive gear, and a huge aftermarket following for it.