Sorry for the delay in getting round to judging. Here it is at last.
Council by Joxeft
Get a coin back after you buy a card. However I think +Buy when you buy a card generally does not work - with cost reduction it allows you to auto-empty a pile, in this case all three trefoil piles.
Three Stooges by fika monster
Interesting, and it's kind of funny how you have to remember to buy different Trefoil cards than the ones you actually want. Ties them together and gives a little bit of command-type flexibility. The downside I see is what happens when there is a big difference in cost between the trefoil piles - eg you could have 6 Grand Market emulators by your second shuffle.
Heads of the Cerberus by LibraryAdventurer
Very thematic (although didn't Cerberus prevent the dead from leaving the underworld?) I assume this is a "in your buy phase" thing, and in setup the trashed pile is chosen at random? A small hurdle to getting access to one pile (and then getting one of them makes it slightly easier to get more of them).
Triple Workshop by lompeluiten
Simple Border Village / Haggler kind of idea, restricted to the three piles. To begin with I misread and thought that gaining another one was compulsory, which I think would actually be more interesting (no I would rather not be getting an extra Chapel with every Village!). But fine as it stands, anyway.
?Three Monkeys? by spineflu
Changes the interaction in the game; instead of attack effects you now have cards being played by everyone. But playing a Trefoil card out of turn is likely to help the active player more than it helps you (as it also lets them play another without using an Action). Fun/complicated in multiplayer working out who's next to make a decision on if they want to play a card!
Triumvirate by emtzalex
A Sauna-Avanto idea is the first thing that came to my mind for Trefoils. This is well-worded, and needing to play them from different piles ties them together well. It seems a bit dominant if one of the trefoil piles gives you terminal draw.
Knot by faust
Good name for a Trefoil (although actually this entry doesn't tie the three piles together as much as some!). Limiting it to only the Trefoil cards that you have in hand at the time feels like an appropriate power level to add interest without making it too dominant. I would recommend setting aside the revealed Trefoil cards to keep you honest and make it easier for everyone to keep track.
Salt, Sulphur, & Mercury by Xen3k
Gaining and exchanging between the different Trefoil cards, which looks entertaining, perhaps even more so if it were compulsory. It's good that it's exchange rather than trash/gain, so the cheaper ones don't run out so fast.
Derby by Augie279
I can't work out if I love this one or hate it. You have to play at least 5 Trefoil cards to trigger it, but then there's a massive jackpot (like horse-racing, right?), so you'll probably try and find a way. Then some combinations of trefoil piles will make it easy and it'll go crazy. Needs clarification on how it would work with split piles. I didn't know what Derbys had to do with '3's until looking on wikipedia, so nice naming!
Lots of great ideas, and several of them became my favourite as I thought about them. But overall I think my two favourite ones are Heads of the Cerberus and Knot.
Cerberus has more going for it thematically, but in the end I think Knot is more interesting more often, so:
Winner: Knot by faust
Runner-up: Heads of the Cerberus by LibraryAdventurer