Trick taking games with the Decktet (like Ace Trump) don't actually feel much like trick taking games to me. Since the number cards are cross suited, you can't lead one to force people to play a particular suit. So you can only rarely play a middling card knowing that everything above it has been played.
Today I had the idea of playing with just the top of the two suits on number cards. This would make it possible to exploit a short or long suit. It would still have some of the weird structure of the Decktet, because there would be different numbers of each suit: 10 moons, 7 suns, 7 waves, 5 leaves, 5 wyrms, and 2 knots. (Only the ace and crown of knots would count as knots, since the knot suit symbol is always printed second when it appears.)
Still, this ignores the second suit entirely. So here was my second idea: After looking at their hands, players bid. The high bidder gets to declare TOP or BOTTOM. If TOP, then cards count as having their upper suit symbol for the duration of the hand. If BOTTOM, their lower suit symbol.
The highest bidder leads. Other player must follow the lead if they can. There is no trump, so high card in suit wins.
The high bidder only gets points if they make their bid, other players score regardless: One point per trick.
Given the distribution for TOP, you'd want to call it if you had a lot of moons, suns, or waves. The distribution for BOTTOM is mirror image: 2 moons, 5 suns, 5 waves, 7 leaves, 7 wyrms, and 10 knots. So you'd want it if you had long suits in knots, wyrms, or waves.
Here are the number cards assigned to each suit, TOP:
Adding pawns, leave out the Watchman. Pawns TOP would be a moon, a sun, and a wave; BOTTOM would be a leaf, a knot, and a wyrm.
This also avoids the complication that arises in Ace Trump, when two players follow suit with the same rank. It can't happen in this game.
I haven't tried this yet, but I guess it would be less random and more like a trick-taking game. Thoughts?