I read your proposal, and could find no details about how a swarm client could actually divide up the task of verification of blocks. That or I simply didn't understand it.
It looks like a node picks a random number between 0 and N-1 and then checks transactions where id = tx-hash mod N.
Who any why? That's the vague part. Are miner's not checking the blocks themselves, are they depending upon others to spot check sections? How does that work, since it's the miners who will feel the losses should they mine a block with an invalid transaction? Realisticly, it'd be at least as effective to permit non-mining full clients to 'spot check' blocks in full, but on a random scale. Say, only 30% of the blocks that they see do they check before they forward. All blocks should be fully checked before intergrated into the local blockchain, and I can't see a way around that process.
Having each new client verify a random 1% of the blocks would be a reasonable thing to do, if combined with an alert system. This would keep miners honest.
But the miners would still need to check those blocks, and eventually so would everyone else. This could introduce a new network attack vector.