Seems like I read at one point someone suggesting use of a private armored truck transport for shipping purposes during a sale process, though I don't remember the full details. It was cas related.
Think that may have been Otoh related... but again, hopefully people read the fine print before hiring a service like this.
Most (if not all) will not cover digital values especially if there are coins with holograms:
Section X, subsection B, part 3:
3. If Your Shipment contains securities, traveler’s checks,
holograms, magnetic strips, credit card stock, data media, computer components or similar items,
Brink’s is
only responsible for replacement cost without regard to information contained on such items, unless the parties have otherwise agreed in writing to have special
terms in connection with such items as set forth in any Rider(s) to this Contract
Seems like you might be able to get a special conditional rider attached to this contract

I think that cost is a bit high for most people and probably overkill. I'm sure there are people here who love to travel that you could hire as a courier to transport Casascius coins if the value made it worth the effort and cost. I'd personally love to be known as "The Transporter" but as someone who doesn't really like to fly around the country it would cost a pretty penny. Still, I think it would be worth the trip just to be referred to as the transporter. So if anyone wants to give me some plane tickets and BTC to have me transport their Casascius coins to a seller, feel free to reach out.