Can Bitcoin Days Destroyed be a better resolution mechanism for competing blocks?
Thanks to Murch, I'm answering my own question; Yes!

Murch made the point that using BTCDD enables a selfish miner to mine a non-broadcast transaction that spends old coins rather than having to rely on a network propagation advantage.  I understand this objection.  That advantage is easily removed by excluding from your BTCDD calculation transactions that you didn't see until you got this new block.  Now the selfish miner has to broadcast his old-coin transaction.

(edit due to comment:) While it is true that some BTCDD-heavy transactions will have gotten to one miner and not another, making the tie-breaking strategy arbitrary, because neither will have the BTCDD-heavy transaction privately mined by the selfish miner, it is still more effective at discouraging selfish mining than letting the network choose randomly, if and when you can assume that most miners will have seen both blocks around the same time.  BTCDD is arbitrary because of incomplete propagation of transactions, but because of fully propagated transactions, it is less arbitrary than first-seen.

Also, you can't spend just a part of an input.  I submit that it's harder to have (enough) old coins than it is to set up a global network of tightly connected nodes for cheating.  I suppose I could be wrong, but old coins is always a dwindling resource and global nodes willing to help cheat is probably a growing one.

The only purpose for orphaning a block is that you've already been mining on top of your replacement for it. This point was made soon after Sirer and Eyal described their selfish mining vulnerability, though quite indirectly.  Using a "later block" to do that would severely diminish the advantage.  The point is to discourage sitting on solutions by making the later block more likely to be accepted.  Would you consider throwing away any seconds of your own mining when you see an alternate solution?  To discourage selfish mining, I'd do a few seconds, I guess.

I also very much like discouraging empty blocks, but who mines empty blocks just to do a selfish mining attack?  Oh wait, that's probably the best way to do it!  Hmm...