I have not used the Perigrines yet, but have some experience with other brands of monolithic expanding bullets. So here is what I can add:

Gyroscopic stability is quite important for bullet accuracy and terminal performance. This is largely determined by the barrel twist rate and bullet length. Note: length, not weight. Since copper has a lower density than lead, mono bullets tend to be lighter for the same length, compared to cup-core types.

For a 1:10" twist 308, I would keep the weight of a spitzer-type mono bullet at 150gn or below. This will not only ensure stable flight, but also help to reduce the risk of a bullet tumbling after impact. Nose-forward penetration is usually deeper and straighter, and helps ensure proper expansion. Do not fall into the trap of using the same weight of mono bullets, as you would have with conventional cup-core types.

Another thing to consider is that mono bullets are quite tough and therefore much less forgiving of barrel tolerance issues. This means that some rifles will just not shoot them well, no matter what tricks you try. So do try them in your rifle, but do not think that accuracy will be guaranteed. Just like their owners, rifles have personal preferences too.