I agree with hashcoin's assessment. An investigator could collect public keys by agreeing to buy from people or pay them for some reason and/or by gaining access to an exchange, pool, or other service that pays people. These people then become easily trackable.

Warning, brainstorm below:

Would it not be better to randomize t instead of incrementing it? Instead you send the coins to h = hash160(concat(c, t)) where t is a large (256-bit?) random number. That way, it seems to me that even someone with public key couldn't determine if a given h was generated from a given c without knowing the t used. Although then again, I don't see how such a transaction could be redeemed by the receiver without some out-of-band communication of t. Maybe you could encrypt t to that public key and insert that into the transaction as well? This would let the receiver be able to see when he received the coins, but in order to prove ownership when spending the transaction, it seems like he'd have to reveal t, giving up the privacy. Maybe some form of non-interactive zero-knowledge proof could be used?