It's important to keep in mind that this refund process wouldn't actually be THAT complicated since the US trade commissions already have those procedures on the books.
There are a TON of ways that tariff payments have to be adjusted under normal times, so those procedures are already part of the system. These refunds would simply trigger those.
There are a lot of folks who say the tariffs might be illegal, but it would be too disruptive to rule against them now. They need to know that it wouldn't actually be that disruptive to do the right thing.