You may yet be able to find a clutch housing (the half of the case that has the bellhousing), 0A4-301-107-AG and of course you'd need the diff itself but may be able to use a used one from something.
Some other part numbers to search:
0A4-300-044 (new gearbox assembly)
0A4-300-045 (updated part number for new)
0A4-300-045-X (reman unit, most likely new though)
Not sure what all is different on the 02J from an A4 and the 0A4 from an A5, aside from the A5s not using a VSS (this signal is instead provided by the ABS controller, which all A5 cars have), and no timing plug (the engines used in the A5 all get TDC set from the other end of the engine). I know there are subtle gearing changes. And it may be enough that the ECU won't like it to the point the cruise control may not work properly, not sure.
Another option would be to swap to a 6sp as there may be more donor cars out there (although a lot of potential donors got crushed with perfectly good gearboxes in them).