simple bribery
Enforce existing laws
support for parties (election campaigns)
Covered in my solution
think tanks
Depending on how the think tank is registered as a business, you can enforce existing non-profit requirements or label them as "political tanks" and make your $100 voucher system include them.
policy advisory boards
Not sure how capitalism affects these types of things. These are largely made up of experts in their field, regardless of how much money they have. Yea they are biased for their industry most likely, but I don't see it as a result of capitalism.
promising of new jobs in return for favours
Already illegal and somewhat taking care of by the voucher system because most of the time 'favors' are just campaign donations.