[Pinkie]

Interesting! If I can get macros to behave properly, I can probably solve the whole thing with the click of a button. Now I know what's going on, I can begin to work with it and see what I can do. I could do an autocorrect to change them as I type, but that would need a space, so it probably won't work. That would be why LO doesn't capitalize after double quotation marks, either.
Some word processors, like Word, the processor that comes with Scrivener, and Softmaker's Textwriter, capitalize contracted words with no problem. I wonder if something could be built in to LO to do the same thing? Because grammatically, that is the correct construct. A period, followed by a pair of closing quotation marks, is the end of a sentence, although a question mark or exclamation mark followed by the quote marks isn't necessarily the sentence's end. I did write a macro to deal with that one, but it's not working properly. I think it may be something to do with the language inconsistency, but I've discovered that if I bake the language into the Style, that works much better.
The Unicode committee should take a look at the Chicago Manual of Style sometime, otherwise known as the Editor's Bible (in the US, anyway!)