Hi Darby, Can't answer all your questions, but perhaps others can fill in the gaps.
No, rudders won't fall out but they will wear more quickly and get even noisier. There's a fair bit of bearing material there; so nothing will get damaged by sailing her south to places that don't gouge sailors quite as bad as they do at Whitsundays. They aren't shimmed. New ones are machined with fine tolerances out of Delrin, Tufnol or whatever the new favourite is, the old ones removed and replaced. Its standard
work for
marine engineering workshops, or anyone with a lathe and vernier calipers.
As you suspect, this usually involves a haulout for ease rather than necessity, as the top of the rudder tubes are above waterline. Usually a
boat is not put onto the hard high enough to drop out and replace rudders. Most yards hold the vessel on the travel
lift or sealift, drop out the rudders, lower the vessel onto blocks/stands, then replace rudder bearing and do other
maintenance. When it's over and time to splash the travel
lift comes back, raises the
boat, up go the rudders, in go the retaining pins and off you go with nice tight rudders.
Even though only the starboard side is bad, I'd do both sides, while you're at it.
Good luck and cheers