I can't comment on the R380 specifically as I have an LT95 box, but I can make some general comments.
Probably the most important point is that all these gear boxes have an oil pump, and this pump will not stand cold EP90 or similar oils - the oil pump drive will shear, leaving you unknowingly with inadequate lubrication. The transfer case is not very fussy about what oil it has, as long as it has enough. As the transfer of oil from one box to another is not uncommon, this suggests that the use of the same oil may be a good idea.
The workable alternatives then are ATF, MTF, or various types of engine oil, and the main differences between them will be in the performance of the synchromesh and general ease of gear changing. Factory recommendations seem to have varied with time. Although not the same box as yours, I am currently using the same oil as I put in the engine (I get it in bulk) with no problems, in both gearbox and transfer case. I have used synthetic engine oil in the main box as an effective cure for difficulties getting it out of first when very cold, but have not continued with this due to the cost.
I think the rubber joint is simply to act as a shock damper when taking up the drive - sort of insurance against ham fisted (oops, footed) drivers.
John
JDNSW
1986 110 County 3.9 diesel
1970 2a 109 2.25 petrol
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