It's not possible for the user to lie since the miner has to report back to the server with the proof of work that they've done.

Hardly any website is going to be willing to require non-trivial proof of work before delivering content. It might work for cutting off a streaming video and to a lesser extent as a gate before allowing a large file download, but it's completely implausible for a text-based article. Would-be readers are not that patient.

You can't; hence you should back it up with tech checking if the user is complying with your requirements.