"Is it possible to remove and replace the moveable part of Elvstrom bailers without taking the whole casing out of the bottom of the boat?"
This is an excellent question, as leaky bailers are almost a given if you have an older boat. Racing in light air in a boat that is slowly filling with water is quite frustrating!
There is a small plate at the forward end of the bailer that locks the valve onto the flange by wrapping around the forward edge of the flange. If you wanted to replace the gasket, you are now ready to do so. If you wanted to replace the valve, you still have to buy the whole replacement bailer unit, but at least you don't have to tear off the old flange and seal in the new one. In my experience, bailers rarely leak at the flange. If you are lucky, you can straighten the inner part now that you have it out of the boat, and put it back in, without having to go and buy a new bailer.
When you are putting either the (fixed) original valve, or a new replacement in, use some soap to lubricate the flange and valve. The valve goes in the reverse of how you took it out. Push the front of the valve into the flange, pushing it as far forward in the flange as you can. Then push the valve up into the flange, and re-install the plastic insert and the bale.
By the way, there are several models of Elvstrom bailer. You need to describe what you want fairly carefully when you order it. Many 505s use the New Large for the larger (usually aft) bailer.