Okay, let's try this... but some cards may really become weak. Or not.
Order of card icons : [top left][bottom left][bottom mid][bottom right]
-Police- (militia like)
[Crown][4][Crown][Crown]
<Crown> Draw a 2
<Crown>I demand, if you have more than 3 cards in hand, that you return cards from your hand until you have 3 cards in hand.
-?
?- (remodel like)
[lightbulb][lightbulb][4][lightbulb]
<lightbulb> return a card from your hand. Draw a card with value 2 higher than the returned card. You may immediatly score it.
-?
?- (wishing-well like)
[leaf][3][castle][leaf]
<castle>Draw a 1, then meld a card in your hand
<castle>I demand you to show me your hand face down. Then I name a card and reveal one of it. If it is the named card, I put it into my hand.
-Corruption- (possession like)
[10][clock][clock][clock]
<clock> I demand you to take an extra turn after mine, in which I can see all your cards and make all decisions for you. Any cards that you would score, I score instead. Any cards that are returned at set aside and returned at end of turn.
-Province- (monument like ; yes, monument is an achievement in innovation, like province is a huge victory card in dominion, so...)
[4][crown][crown][factory]
<crown> draw a 2
<crown> gain a Score token
(assume there are score tokens worth 1 score point each and once you gain them, they can't be taken back. If you don't like this, you can replace it with : "draw a 1 and score it")
-?
?- (horn of plenty like)
[10][clock][factory][crown]
<clock> draw, then either meld or score a card of value equal to the number of your different colors on your board plus the numbers of resources you produce at least 3 copies of. (e.g. if you have 5 colors and produce 5 resources with at least 3 copies, you draw a 10 and choose to meld it or score it ; if you have 5 colors and produce all six resources at least 3 times... end of game, so you've got to score !)