The Good Judgement Project (for that was its name) is pretty awesome - but if you mechanically connected it to the policy apparatus, I'd expect Mr Goodhart on the next train.

You've proposed a few possible countermeasures (play money, publication of bets, a guess at the equilibrium outcome of a vastly complex HFT game). Each of these might work, but (a) isn't actually what Robin Hanson is proposing (b) hasn't been tested as a defence against highly motivated adversarial actors.

And they would be motivated. The threat model here is "manipulate this market and directly influence policy in your favour". They say "money in politics is like water - it finds all the cracks", and politics at least has humans in the loop. The track record of people betting against it is...not promising.