I agree with the first point of your message, but the staff in AMS have told me several times that Plat/Ulti no longer get arrival benefits at the lounges. I've also only scanned the boarding pass of the next flight on the next morning while entering the lounge.

Of course, it's quite possible what you say is why it happened. But the rules technically say that as long as you're in connection, then there's no time limit for how early you can arrive and stay in the lounge. Only on departures there's a 3hr rule now. So I'd hope it works for the OP as well. But, if somehow the system ends up treating the two flights as completely separate, then you're absolutely right, and unless OP is Gold/Plat/Ulti, they will have to wait to enter the lounge 3hrs before.