The details are here: https://www.cbp.gov/trade/programs-administration/entry-summ...

And

https://content.govdelivery.com/accounts/USDHSCBP/bulletins/...

And you use the ACE system to set everything up and report origins of melting, etc and it computes the fees for you:

https://www.cbp.gov/trade/automated

From your first link:

> Does CBP require an aluminum certificate of analysis to be filed at the time of entry? > > At this time, CBP does not require an aluminum certificate of analysis to be filed at the time of entry. CBP, however, >>> can <<< request the importer to provide an aluminum certificate of analysis if CBP needs one to ensure compliance with the entry requirements pertinent to the item being imported.

In other words: they usually trust people to file their paperwork correctly, but reserve the right to demand lab reports when they suspected foul play. Filing lab paperwork in advance is not needed, however.

As mentioned in Olimex's blog post: US customs is now starting to ask everyone for a Certificate of Analysis. Paperwork isn't enough anymore, even when it is an obviously harmless product which has been imported many times in the past without any issues. If you can't hand over a lab report, it's not getting in.