I apologise for taking so long to get around to providing my comments on the remaining submissions. I've unfortunately been quite busy in the past few weeks.
My thoughts are below:
kru5h - SmeltingGet +1 Buy when you play Gold.
Smelting makes Gold a lot more attractive, and by extension any gold-gainers. I wonder if this would monolithically favor money strategies, which in my opinion, makes this less interesting. I think this could be more interesting as a Project than an Edict.
segura - MonarchyAt the start of each turn, gain a Copper to your hand or discard a card.
This probably could have made the shortlist, but unfortunately I don't believe segura clarified if they really meant at the start of each turn, rather than at the start of your turn (or each of your turns). As worded, I think makes the Edict quite oppressive in games with more than two players. Even if it only applied to the active player's turn, I don't think this would be everyone's cup of tea since it could potentially turn games into slogs. Nevertheless, I still think this would create some interesting decisions at the start of your turn.
naitchman - Lucky FindYou may not buy a Rare Card if you do not have any Luck cards in play
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Setup: Randomly choose a Kingdom pile for which no other Kingdom pile costs more. Cards from that pile are Rare Cards. Randomly choose a different Action or Treasure Kingdom pile for which no other Kingdom pile costs less. Cards from that pile are Luck Cards"
At first glance, the small text is a bit off-putting, but I think there is an interesting idea here. It takes a bit of extra setup at the start of games, which isn't usually a problem as long as the additional set up is worth it. Only being able to buy Rare card if you have a Luck Card in play is intriguing. However, the specific combination of Rare Card and Luck Card may not always lead to interesting decisions in terms of when to buy them. For example, if the Rare Card happens to be a a fairly undesirable $5-cost card then that is much less likely to factor into your decision of whether to buy a Luck Card. My other concern is that if the Luck card isn't one that you would want to have many copies of in your deck, then it could make buying the Rare card quite undesirable (it's almost like tacking a Potion cost on the card). There is also a scenario where the Luck Card happens to be Embargo or Acting Troupe, which pretty much makes it impossible to buy the Rare card in games without Ways (although you can still gain it through workshops or remodelers).
grrgrrgrr - Other DimensionWhen you'd normally get +Actions from anything other than Villagers, you get +$ instead. When you gain a card, +1 Villager
Other Dimension looks wacky and potentially fun to try; however, I fear it may be too game-warping. The original version that gave +Cards instead of +Actions was probably broken; the revised version that gives +$ instead of Actions is much better. Since every Action card effectively becomes terminal (although you could argue that all gainers are non-terminal), managing terminal space becomes a different beast. I think Kingdoms without extra gains would really fall flat with Other Dimension. I also worry that this would throw off the balance of existing cards. Other Dimension could work in a curated Kingdom, but I don't know if this will work well for any random Kingdom.
mathdude - RationingThe game does not end with 3 empty Supply piles, but with 5.
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Setup: for each Kingdom Supply pile, use only half as many of each uniquely named card as usual (rounded up)"
Rationing introduces some rules twists, making less Kingdom cards available to players and also altering a game-end condition. I don't think this would work well at higher player counts, but it is probably fine for 2 or 3-player games. I'm not sure if I would enjoy games with Rationing more than normal ones. It probably forces players to build their decks with a higher variety of cards and discourages monolithic strategies like a Minion stack, but it will often make building an effective engine harder.
NoMoreFun - HerdingWhen you gain a Silver, you may exchange it for a Horse, and vice-versa
In Kingdoms without Silver-gainers or Horse-gainers, Herding would be like having Ride available as an Event, except it would now cost you $3 for a Horse instead of $2. Herding is a lot more interesting and looks quite fun when you have Silver-gainers or Horse-gainers in the Kingdom, but unfortunately I think the majority of Kingdoms will not have either of those. You often don't want too many Silvers in your deck, so Herding significantly buffs cards like Bureaucrat, Trader, and Jack-of-all-Trades. Having the option to gain Silvers from your Paddocks or Sleighs for extra payload would also be nice.
Shael - AlchemyWhen you buy a card, you may overpay any number of Potion for it. For each overpaid Potion, gain two cheaper non-Victory cards
Alchemy gives you a reason to consider buying a Potion, even if there are no Potion-cost cards in the Kingdom. Potion is now a non-terminal Haggler variant, and I think the effect looks quite good (possibly too good) for a $4-cost Treasure. Since you can choose whether or not to overpay with Potions, you don't have the same potential drawback as with Haggler or Talisman where you may be forced to gain cards that you don't want. I'm not entirely sure that this needs to be an Edict rather than a separate Kingdom card.
spineflu - UrbanizingWhen a card gives you +Actions, you get twice as many
Urbanizing will effectively turn any non-terminal Action card into a village. I don't think that having an overabundance of +Actions will necessarily make games more fun, since puzzling out how to manage your terminal space is one of the things I like about Dominion. I also have a similar concern as with Other Dimension that this could disrupt the balance of existing cards.
Aquila - UnderlordsAt the start of each of your turns, you may trash a card costing $2 or less from you hand. If you don't, gain such a card from the trash.
Underlords almost made the shortlist. It will allow players to thin their decks fairly quickly and so will tend to accelerate games. If players don't have any junk in hand to trash, they instead must gain a cheap card (usually junk but not always) from the trash. The decision of whether or not to trash a card from your hand will not always be automatic - for instance, if you have 5 Coppers in hand, it won't always be clear whether it is more optimal to be able to buy a $5-cost card (and be forced to gain junk) or to trash a Copper and buy a $4-cost card. There could be some interesting interactions in some games (for example, with cost-reduction you could gain Zombies or other normally more expensive cards out of the trash). There could be a risk of slightly exacerbating a first player advantage during the opening (for example, if player 1 has 5/2 and player 2 has 2/5), but I don't see this as a major flaw.
The Alchemist - AsceticismWhen you gain a Copper, Silver, or Gold, return it to the Supply and +1 Coffers
The concept of not being able to add non-Kingdom Treasures to your deck is an interesting one. I think one issue, as others have pointed out, is that it could tend to prolong games especially if there aren't any Action cards in the Kingdom that give you economy. Another issue is that if you have lots of +Buy available, I think it makes gaining Coffers fairly trivial, as you could convert all you unused Buys into Coffers. I'm also not sure I like the fact that it nerfs gold-gainers and makes it harder to keep Encampments in your deck or to active Legionaries. I liked the Urbanization Edict (which replaces a starting card with a Silver) better.