BH – We’ve taken that route twice. Last time was Aug 2019.
The layover going over was long (12hrs) but, the secure area of the terminal is very large, lots of shops and restaurants. We booked a day-room in the
Yotel Hotel right there inside the second floor of the secured area. Since we’d both been to AMS and the city, we just decided to stay in the airport. Not even sure you can go into the city now with the Rona even. We had a shorter layover on the way back and the Yotel also offers just shower booths. We did that instead of the full Yotel Hotel room on the way home.
You do have to apply for a transit permit for firearms even though they are checked all the way thru. The form is kind of long but the instructions (English) are pretty clear and easy to follow. You fill it out, print, sign and scan it back in and email it to the terminal security officials along with a copy of your passport, 4457, airline ticket and PH/Outfitter's Invitation/Motivation letter. Kicker is you must submit it 8-WEEKS before your initial transit. It covers your return flt home. No fees.
They will not issue the permit until the week before you fly. You will receive a confirmation email they received your application. If they have any questions or need corrections to the form they will contact you by email. May want to start tickling them once a week a month before you depart. Your actual permit will be just a counter-signed copy of your application with some official stamps on it. Print it, put a copy in your rifle case(s) and keep a copy. We just had to show a copy when we initially checked in with Delta and KLM on the return trip home.
KLM also has a simple one page firearm declaration form to fill out and give to the check-in agent.
I can send you a copy of the forms or you can download them from the KLM website.
All in all the flights were good and would go this route again based on pricing.