'Tap target permanent' seems disproportionately strong compared to the other two abilities.

While I agree, I think that's a way of saying "the first two abilities seem disproportionately weak".

My major beef with this card is that it will rarely be used in the most powerful way. You want to be tapping your opponent's blockers or attackers with this, but many unhappy over-cautious players won't advance the game state because they're afraid that their opponent has a kill spell, and won't activate this ability for fear that it will happen. How frustrating.

I'd suggest either changing the Hexproof to something else so that the other two abilities get played, or removing the tap ability and replacing it with something you can activate at end of turn.

I will agree that the first ability is weaker than the last two. I don't know that it outright prevents players from ever wanting to use the other abilities though. The Wizard archetype within the set tends to be about active optimization of your creatures, and a reactive ability like granting spot-protection doesn't really fit that bill.

Whether offering two other abilities prevents a third "best" option from being used though is, I think, less of a problem. The whole purpose of a charm or UtiliRune is that it offers flexibility. Is the tap ability strong? Yes. Quite possibly too strong. Is the bounce-an-aura too weak? In this environment, I strongly doubt it.

But that still leaves two questions: what to offer the Wizards as an option, and how to amend the tapping ability.

I wasn't convinced that it was that much more powerful than the other two options, either. I was just using the momentum of the other two posts to build on my argument. Forgive me. Sometimes I use unfair arguing tactics.

Though, on reflection, the easiest way to solve this problem might be to give the enchantment "untap" as opposed to "tap". That way you can still threaten to use it to untap a blocker, in the same way that you're threatening to use it to give a creature Hexproof. Plus, I think you might be able to use untap a bit more at the end of your turn. If you're that defensive a player, you probably already are playing a lot of reactive instants.

I think what my contemporaries meant when they said "The tap ability is better" was probably "the tap ability will be used in every game of Magic you put this card into." which is true. The same can't be said of untapping, though it is a powerful effect.

I've "dampened" the tap ability so that it's situationally useful as a combat trick, but still potent in a "taxation control" deck. I'm still not entirely happy with the first ability though, mostly because I've already got Haze Veil at uncommon.

Moved away from wizard tricks altogether and gave blue mill some love.

Ah, yes. My brow is now unfurrowed.

readjusted once more for new environment.

Again, the name feels awkward to me: maybe Theurgist Charm?