Trying to fit a Blackburn EX1 rack to my bike
I've never heard of a problem with P-clips. They are the standard way to mount a rack when the bike doesn't have upper rack braze-ons.

I don't see how the P-clips can slip. The rack you're using is solid, not hinged, so if you only mounted it to the fender eyelets, it could only rotate forward/backward around that point. As soon as you locate it with P-clips as well, there's nowhere for it to slip.

It might be possible for the nuts and bolts you use to affix the P-clips to come loose. You can use nuts with nylock inserts, or just retighten them as needed.