Mike,
The physical size of the 5 speed Supra box doesn't appear to be a problem. Rod Hadfield at Castlemaine Rod Shop
www.rodshop.com.au will definitely be able to supply a bolt-in bellhousing/adaptor for the LS1 - Supra.
My worry would be how far back the shifter is.... I think my elbow would hit the rear firewall behind the seats when going for 2nd or 4th gears! I wonder if you can relocate it?