I've got a turbo trans I'll sell you for much cheaper than that ($250). I pulled it because the syncro's are pretty worn and because I had an S2 trans (better gearing for a 951) to put in it. Syncro's and bearings are fairly cheap (even on Pelican parts) and I was thinking of refreshing this one and putting it up for sale, but if you need a core to work on, I'll help a brother out.
If you've refreshed a 5-speed before you shouldn't have too much issue as the "special tools" can be fabricated if need be.
BTW, the factory cooler is a joke and like the Turbo brakes, adjustable suspension pieces, etc is only there for homologation purposes (or to get people to pay more for the cars) as most serious racers replace the useless pump and cooler with a proper one under various sanctioning body rule loopholes. Go ahead and buy yourself a differential cooling pump, thermostat and cooler. When you have it apart just drill the case for the fittings and get on with life. Here's an idea: http://www.gt40s.com/forum/gt40-tech-powertrain-transaxles/26642-audi-016-oil-cooler.html
As for installing the limited slip. There's a couple of choices:
1) Factory limited slip, grab any 924/944 016 transaxle with one in it, refresh it and install. Parts are listed on the PET catalog and aren't too bad to buy.
2) Guards Limited slip, not cheap but would be brand new and ready to install. http://www.guardtransmissionllc.com/products/limited-slip-differentials/
3) Audi V8 Torsen from the rear of the Audi V8 Quattro Sedans, cheapest solution, more well suited for the street, requires machining one side of the diff down to fit the bearings in the 016 case. http://www.924board.org/viewtopic.php?t=23820
As for installing whichever choice you go with, there's a really good write-up/walkthrough here:
http://rennlist.com/forums/944-turbo-and-turbo-s-forum/686949-944-transmission-walkthrough-image-heavy.html
The gist of it was that basically you have to disassemble the case to remove and install the differential and you get to do this several times to set the preload on the carrier bearings and if you change the final drive, you'll have to set the pinion depth as well.
As for other things to do while you have it apart? I'd look into adding a stiffening plate to the rear of the transaxle:
http://www.gt40s.com/forum/gt40-tech-powertrain-transaxles/23387-audi-016-reinforcement-plate.html
http://stweb.peelschools.org/sssweb/TTI-WEB/cars/pictures/AudiTransaxleUpgradeStepbyStep/index.html
You can buy the plate here: http://www.texasperformanceconcepts.com/Conversion-parts.html
Hope this helps!