A problem with this approach is that the block will contain a coinbase tx which includes a recipient address.

Everybody wants to be the recipient of the block reward which will entail changing the recipient address, which will change the hash. Also, as achow101 pointed out, you can not "aim at" a particular hash. The amount of currently done work on a block could give miners a clue as to what other miners are mining, but I don't thing they would find this information particularly useful.