What's to discourage the cattle owner from claiming their cows produce no methane due to seaweed use & then collecting the cap and trade/carbon tax benefit while not bothering with the seaweed?
More broadly, how does cap and trade/carbon tax measure the footprint of a business in the first place? I've found no material on the subject but my guess is that they do it based on the power plant/fuel you're using & how much energy your using. Not sure how they measure gases as a byproduct of industrial processes but maybe that's minuscule?
The possibility of an IRS audit would discourage lying about it. If you're claiming to be feeding your cattle seaweed, you're going to have to buy it. Just like any other business expense, you'll need receipts. And once you have the seaweed feed, you might as well use it.
To be honest, I'm not sure how the emissions measuring is done, but I think it's handled on the supply-side for fuel and electricity in existing implementations. Suppliers just pass on the cost of taxes. For direct agricultural emissions from cattle, you could probably use an estimate based on the average emissions per cow, and provide a deduction based on feed. Maybe with an exemption for small farms.
Farmers could buy their seaweed from Acme Agrisupply, SuperKelp(TM) "made with 100% seaweed" (3% seaweed by weight, 97% corn filler), which costs 1/10th the price of real seaweed.