If there really was anything the public could do to stop such abuses of power by the bureaucracies, they would have been used to stop Bensen's shotgun ban (which the NRA or GOA would have attempted) or the HHS HIPAA regulations (which a huge number of medical, insurance, and software companies, not to mention privacy groups, opposed for very valid reasons).
Mere opposition does not a bad regulation make, there has to be a material error, malfeasance, misfeasance involved for challenge. If what is done is within the scope statute and in common practice of the art, or legislatively mandated methodology. Then you are out of luck unless Congress or the President makes the challenge by shooting the regulation down.
Intent of the statue as expressed within the language of statute is the key to a challenge at the judicial level. If a proposed statistical value, which is what is under discussion, can be shown to be erroneous in regard to the historically adopted standard or legislatively adopted standard. Then you have a decent basis for challenging the result.
In terms of your examples legislative intent was not an issue, nor a statistcally absurd CPI value which is what would be required to send a $150,000 FCA to anyone. A CPI error of the magnitude it would take to implement such a scheme is totally irrational. It would be totally irrational to see an advance of of even 3 standard devieations (21%) of one year's FCA over the current year much less an advance of some 15,000%. Any increase of FCA would also entail the increase of the NRST tax rate to compensate. A factor that would hit everyone right in the gut at much lower levels than your absurdity.
But then why not just some bureaucrat go out and start sending 150,000 checks to everyone, and not bother with FCA or the CPI. By your reasoning, no one would or could do anything about it so that bureaucrat can just as well go ahead and do it and be acclaimed a hero for buying a landslide victory and turn the country over to the communist party.
You reasoning is not just invalid, it is just plain absurd.