I made that suggestion a few times.  If miners could broadcast near misses, then the network should quickly converge on one of the 2 blocks, when there is a tie.  Even if some miners don't broadcast, the ones that do would give faster convergence.

For deterministic mining, you could use something like

weight_block_n = [sum(all blocks in the tie) + hash_block_n] mod Target

Pick the block with the most weight.  

This makes it so that a miner can't determine if they will win a tie, in advance of the 2nd block being found.  This keeps the incentive to broadcast as quickly as possible.

I am not sure this counts as the selfish mining attack.  I thought that assumed that the attacker had better network connectivity to the victim?  Even a slower miner would win the tie break in this case.