I start in a different place and end in a different place. I start with the idea that the UBI should be taxable income. I justify the UBI as a national dividend, and so I would tax it as such. So, for anyone filing a tax return, add $12k to the Qualified Dividends line (or a special line on the 1040-EZ) and subtract $12k from your final tax bill.
If you have a steady job, the after-tax UBI would be "paid" in the form of reduced withholding. If there are two recipients in a one-earner, joint return household, all of that can be handled on the W-4. The point is that the employer administers the payment, saving on costs at the government level.
People who cannot extract the UBI as reduced withholding can do the same thing with their estimated tax payments.
Those whose total tax bill will be less than their UBI can estimate a negative tax and receive monthly credits to their bank accounts or a government-issued debit card.