I am surely moving the goalposts here, but would it be possible to amortize the verification over many blocks?
Sort of a distributed partial Rabin-Miller (is that practical and can it be made provable?)
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It all hinges on the provability of a partial Rabin-Miller test, which may be a pipe dream

This looks like a job for a pool where state across multiple miners can be maintained. Maintaining validation and reward allocation across a distributed network would be PhD material.