At this point in my collection, I only want games that are completely different from the ones I already have
Then you should definitely try Zendo! There's nothing really like it (except the card game from 50 years back that Zendo itself was derived from).
Note that you don't need to track down the game itself... just read through the rules and you'll see that it can be played with many different things (dice, coins, words, you name it--we play with Legos, three sizes and four colors.)
Carolus Magnus comes to mind in that regard, too...