The block producer makes sure his partition (the one he is validating) is valid. Thus he will never lose his block rewards. He marks the block as only guaranteeing the partition(s) he has validated, so any other partitions included are informational but not Nash equilibrium confirmations. Re-read my prior post with that in mind. Again this is only valid for strict partitions (no cross-partition) transactions system.
I think my point still applies. What is his incentive to include more than the single partition he is validating in his blocks?
He has to implicitly (whether or not he includes the latest update to that other unvalidated partition) when he builds his block at the end of the chain that includes that other unvalidated partition. Longest chain wins so he won't want to ignore that last block. His block reward doesn't hinge on whether that latest (before the current or new) block contained a valid partition (assuming it is not the partition the current or new block is declaring to be valid).
Convoluted to write, but not convoluted in my mind. Seems quite simple. Some of the convoluted stuff on the 140+ IQ level of a Raven's matrices IQ test is more convoluted.
Edit: think of it as multiplexing while maintaining a holistic Nash equilibrium.