SteveThurs said:

The variables that decide how a cross-border order goes are declaration wording, the destination country's import rules for prescription medicines,…

International shipping tracking for cross-border ordering orders: my experience with customs in the US when ordering from overseas:

Required FDA import alert review, delayed 10 days.

Tips: always include a copy of your prescription, declare medication properly on customs forms, keep quantities reasonable (personal use = 3 month supply max), and use a vendor who has experience shipping to your country.

A narrower follow-up, since the general answer is now clear:

What actually works on a prior-authorisation denial, as opposed to the list of things that sound like they should work?

anders_CPH said:

International shipping tracking for cross-border ordering orders: my experience with customs in the US when ordering from overseas: Required FDA…

My experience ordering cross-border ordering internationally: I've ordered from a UK pharmacy. Customs can be hit or miss.

Shipping time: 7-14 days
Customs clearance: smooth, no issues
Quality: Janoshik tested at 98.4% purity

International ordering adds complexity but can save 60-80% compared to US prices. Research your country's import laws first.

Closing the loop on my own question.

Follow-up — getting the denial reason in writing was the step that mattered. It named the criterion, and the criterion was a document I already had.

LipidDoc_ATL said:

My experience ordering cross-border ordering internationally: I've ordered from a UK pharmacy.

Fair, and it stops being fair at the extremes. The middle of the range is well understood; the ends are where the honest answer is that nobody knows.