If one was to be able to borrow an original T44 (a long shot) how involved (expensive) would it be to make a mold or cast of the outer case? Once you have that would building the internals still be a challenge or would new parts fit into it?
I think we get about $5000 for a full unmachined casting set. (6 mag castings for the case/shifter/top, 1 aluminum bellhousing, 5 brass shift forks) Then you need several custom pieces including a custom ring and pinion. There's a reason new T44 boxes are more than $25K (Maybe more than $30K...)
As far as putting different internals in a modified case, check out the long thread on making your own gearbox.
If you're just after it for the looks I'd be very tempted to create a fibreglass mold round the original, add an 'inner' from the gearbox you plan on using and cast using a resin/metal powder mix (cold cast metal). I'd suggest an oil cooler would be essential if taking this approach as it would probably make quite a nice insulating jacket!