Home Made Easy 8-3/4 Center Chuck Storage

IMO one bucket would be enough if you just cut up a cardboard box and put 5 orso layers on the bottom of the bucket, lower the 3rd member in it and put the cover on for dust protection.
The cardboard on the bottom cushions the load of the gears a bit and also acts as an oil catcher, as a fair amount of oil will always drip out of these things when stored.

Personally I'm using 6 nuts and 3 pieces of 3/8" all-thread attached, which are long enough to just hold the 3rd member off the ground with the gears down.
As for carrying a 3rd member around (before installation for instance) I use the u-bolt part of a 2.5 of 3" exhaust-tube clamp, mounted in one of the top holes of the 3rd member so it can be carried horizontally.