Do you have someone at the rec'ing end also paying a chunk on those funds exchanging dollars into whatever? I don't think your average illegal who doesn't speak English is going to find it all that easy to work with a bank to do the fancy shifting you suggest--although a black market would likely emerge. They'd either pay the tax or send the currency in the mail.
There's is also the "critical mass" factor which would figure into haggling the percentage. Whatever the market would bear.
Do you realize that those billions do not remain in our economy? It goes straight out.