I use chess pieces. It's not all that different to what you are doing with
magnets except that I think it meets the objectives you state in your message.
Partners are same pieces of a different colour (e.g. a pawn's partner is
a pawn, etc, and you only use one pair of pawns). You can use black to
represent Larks etc (or the other way around obviously). Couples are
arranged in some meaningful order to you, such as by the value of the
chess piece or by height.
Then after you move them all around for a while, you can still tell who's who.
Actually I bought four different colours of chess pieces from
(five years ago, so things there might have
changed). I've never used them to play chess. (I had in mind to make a
youtube video about how some dance progressions work, which I may or may
not manage to do some day. But I've used them to work out dances a lot.)
ajr, dancing in and near Toronto, Canada