Lyminster Halt
I just plain missed Kingston on Sea, but the Hove situation is more complicated. The original Hove station seems to have been very close to Holland Road Halt, and there was yet another station called Cliftonville which was just east of current Hove (in fact the current station is probably a westward extension of Cliftonville as I understand it).
Incidentally there seems to have been a similar kind of situation at Lewes, with stations called Ham and Pinwell shown in one of my sources, but I couldn't find out enough to be confident in naming them. Maybe you all know more.