I find it easy to remove the frag from plugs and discs. If the frag is going to be incrusted then I would rather have it on rubble. I have never recieved frags upside down on styrofoam but it sounds like the best method.
Depending on the tile used, I prefer mounted. For those corals I mount, I personally use white marble tiles. This is basically pure calcium carbonate. Research and experience have shown this to be an almost ideal growing substrate. Many if not most corals will utilize elements from the substrate they are growing on, and this provides a beneficial medium. I've anecdotally seen a greatly increased rate of growth and attachment with these tiles. That's my reasoning. If it's going to be ceramic or plaster, I'd prefer unmounted, though it's easy enough to remove most frags and remount on my own tiles. Really, though, I've rarely had any problems with shipments caused by the method or materials used to mount. I've had lots of shipments with various plugs, tiles, rubble, and free, and when properly packed and healthy all arrive just fine.
More often than not, problems are the result of the conditioning of the coral frag, not the shipping. I've had corals come through all kinds of conditions and pull through. It's the corals that are freshly cut and shipped that seem to have the most problems. The double stressor of being fragged and then immediately shipped causes most of the problems, IME. I prefer to frag my corals several days to weeks ahead of time, depending on the species. This gives them some chance to heal and build energy reserves, etc, and reduces the chances of death from stress or infection.
I have no problem doing as others have suggested. I grow the frag out, frag a piece off and mount in my place of choice, and keep growing the old frag for trades and such.
Mounted to discs, floated upside down with styro. I've yet to receive a shipment of unmounted frags where there wasn't significant damage to at least one of the pieces.
I like the sps on plugs. That way I can put them on the frag rack out of the sand. zoas I like on rubble. Chalices on disks and acans unmounted. So i guess they all have their purpose to me.
another for unmounted sps. I like to mount those direct in the display. I have gotten some zenia and softies over the years flosting with styrofoam which works well for shipping. other than that plugs please. I love the rock looking plugs from fish heads but I am sure they are pretty expensive.
Terry
Mounted to frag plugs if a smaller frag, frag disc if it's a larger frag. I keep my frags in egg crate in my quarentine system for treatment and observation, then move them onto a frag rack in the display until they adjust to the tank and I find a good spot for them.