Yo Bro,
http://www.gtr.co.uk/forum/112571-r34-gtr-...ice-manual.html
The Supra gearbox is apparently near identical internally to the R...
http://t24ever.com/docs/fsm/toyota%20v160%...al%20RM351E.pdf
(Page 13 shows a cutaway diagram of the box)
Based on this diagram (much clearer) If you dropped the nylon carrier into the area where the shifter is, it appears to be very isolated from the drivetrain area itself? It may only have a small amount of oil flow into there to lubricate the mechanism, but if the oil feed is small the nylon cup probably wouldn't migrate into the main gearset area. Don't take my word for it though let RPM be the authority
Good luck with it!
EDIT: Another idea I just had, did that area under the shifter where you said there is an immersion of oil, drain away when you removed the main drainplug? Perhaps you can stick a syringe or fluid pump with a long plastic hose extension down there to suck all the oil out. Based on the picture there does not seem to be much in that area. Once the oil is out you should hopefully be able to see the nylon cup then remove it using one of those handy mini claw grabber tools.