Preposition trouble

[rhu]

Over lunch with the kids, I was explaining how a "squirt dolphin" works. (It's a water pistol for parents who don't want to encourage gunplay.) I said:

It squirts water at whomever you aim it...

and then I froze. My pending-preposition-reference-count was non-zero and urged me to say "at," but my don't-end-a-sentence-with-a-preposition hemisphere said, "uh-uh, the place for that 'at' was four words ago." So I tried again:

It squirts water at at...

Ugh! I stopped right there. This isn't an ack-ack or an atlatl, it's an English sentence.

Forgetting about awkwardness, the grammatically correct structure would be

It squirts water at at whomever you aim it.

introverte says the second "at" should be elided and my original sentence, where I stopped it, would have been fine. This is clearly a problem only because both prepositions are the word "at". Compare:

It steals bananas from at whomever you aim it.
It squirts water at from whom you've stolen bananas.

So, ok, I recast the sentence completely:

It squirts water at the person at whom it's aimed.

and since I feel the passive voice is too often maligned, I'm satisified with this sentence --- but I still want to know if there's a deeper reason that "at at" feels wrong.

(WedNYT 7:08)