One issue I can see unless I've misunderstood.
When the winning block on the Bitcoin network is published, what's stopping me picking that up and publishing it onto the sidechain, even if I didn't mine it.
Indeed, the devil is in the detail. Good point! Thanks for bringing that up
The easy solution is, as a requirement, the side chain block must be signed with the private key corresponding to the bitcoin address of the winning miner (or runner up). In the case of runner up, it's not really required since it will not be published as opposed to the winning block as you stated.