I'm not hugely worried about any ammo currently produced in the United States in any gun currently produced in the United States. That said, I would strongly suggest keeping BB "+P" to a minimum. In the absence of a .380+P spec from SAAMI, it makes sense to err on the side of caution.
Two points here:
1) In truth, all pocket pistols are always about shot placement, regardless of the ammo. Whether .38 Special, .380, .32, even .22LR from something like a TPH, we ABSOLUTELY have to rely on shot placement for them to deliver the mail. I'm not sure that kicking an anemic round up a 100 fps or so changes anything, and it makes the NECESSARY second and third shot that much harder to place. I know for a fact that I can precisely place multiple shots with the LCP with either Cor-Bon or Winchester SliverTips, and that knowledge is more valuable to me than a bump in fps.
2) With pocket pistols, we need to practice with ball. Better yet, we need to find an equivalent gun in .22LR and practice with that. Pocket pistols are unpleasant to shoot...DUH...and it's far too easy to generate a raft of bad habits. I know there's a whole school of thought about "only shooting what you carry," but that runs smack against the fact that training with .22LR or even AirSoft yileds huge gains...heck, remember that Tasuya Sakai won the Steel Challenge by spending a year in Japan shooting only AirSoft. SWAT teams and Special Forces routinely train with sims. We should take a page with what works. I'd love an LCP in .22LR...I can;t say Ruger is enthused about the project!
Michael B