If so, how do I apply a saved table to the new installation? I have quite a number of custom replacements.
Just keep you user profile, and you will have everything, not only autocorrect, in place after an upgrade.
You can even keep your personal autocorr settings totally different from installation paths. Make a folder for it, e.g my_autocorr. Then goto Tools > Options > LibreOffice > Paths. Select Type AutoCorrect, then click on button Edit. Now click button Add. Choose your folder.
You can have several paths at the same time, but only one can be the “Default Path”. That means only this folder will be writable. BTW, here you see, were your normal autocorr informations are stored. To save them, copy the whole folder.
You need to restart LibreOffice, for to make the changes effective.