I went to a talk and toured a US national lab working on this. They were using the slower method that this paper mentions. What struck me most about their process was the overall simplicity. One researcher went to goodwill, bought an old sweater, impregnated a sample of the fabric, and started capturing uranium in the span of a few hours.

They walked me through a cost analysis that borrowed methods and tools from commercial oyster farms. Roughly 50ft lines of prepared binding material would be anchored to a weighted line and buoyed with small floats. Long rows would be unspooled of the back of a boat, left to soak for a few weeks, pulled back in, rinsed with a mild acid, only to be put right back out again. Their calculations showed that they would yield yellow cake at 2x the 2018 market rate. This was in non-ideal conditions, namely slow moving colder water. They expected an increased yield from warmer fast moving water.

Last I talked to them, they were working with desalination plants to see if it would be feasible to post filter their brine. Preliminary cost projections indicated that they might be able to hit competitive pricing, and that was 2018 numbers. The market rate has since doubled.