I have a P1 that I bought many years ago, it has a tapered barrel and iron sights. It is factory marked for both .308 and 7.62 I have used both types of ammunition and have had no problems at all. It is a tremendously strong action so I wouldn't owrryabout using NATO ball if I was you, though you do appear to have a P2Cool, thanks for the confirmation. Yeah I had already found out the 308 has a fractionally thinner case and higher chamber pressures, and you can use a NATO round in a 308, but not the other way round.
I've already bought some thicker walled NATO cases, but nice to know I can use the cheaper 308 cases next time round... and agree, she shoots beautifully. I had some milsurp ammo to test it with and was practically putting them through the same hole at 100m. 😀