Every N seconds, publish a "generation" string, randomly generated. This string must be prefixed to the nonce of the winner of the contest for [marquee, color, grid square].
When performing the "winner test" for new submissions, before the comparison to find out which is less, both the challenger and incumbent hashes are subject to the operation H << M where H is the hash and M is the age of their generation string (current = 0, previous = 1, second-previous = 2, etc.). This means incumbents weaken over time unless the incumbent's submitter continues to defend them by brute-forcing with newer published generation strings.
Since the hash (SHA256) is 256 bits, you'd need to keep 256 previous generation strings, and this could get a bit expensive for testing new submissions. But computers are pretty fast nowadays!