One of our guys experienced repeated stoppages when trying to use his then-new LCP for the first time, even with ball loads.
When he asked for some assistance, I told him to shoot a couple magazine loads while I closely watched his hands/grip from both sides while he was shooting the little gun.
He favors a thumbs/forward grip where both thumbs are located high, relative to the slide.
While he couldn't
feel it happening during the abrupt, snappy little recoil impulse, it wasn't hard for me to see that at least one of his thumbs was tightening and hitting against the slide during recoil & cycling. That little slide doesn't travel far, and it really needs its full freedom of movement without any added resistance of a thumb touching it during cycling.
While I could tell he wasn't quite willing to believe he was unintentionally thumbing the slide (since he didn't feel it happening), he adjusted his thumbs ... and the "problem" immediately went away, with both ball and JHP's.
Reminded me of how some guys with fleshy hands could manage to slow slide velocity in the older PPK's by having the slides run across the web of their hands (except they'd know that was happening by either feeling the cutting of the skin, or seeing the "railroad track" red marks, across the web of their hands).
Another thing to consider is the ammunition being used. You didn't list the ammo, but if it was one of the hot-rodded loads offered by someone other than one of the major American ammo companies, I'd try something from one of the major makers to rule out an ammo-related issue.
It's not unknown to have feeding stoppages, or other functioning issues, occur if the ammo is either under or over-powered.
The .380 is what it is, and what it
isn't is anything other than a .380 ACP. It's not a .38 Spl, for example. At least .38 Spl can use heavier bullet weights, and many of them are rated and approved for use with quality +P loads.
I've tried an assortment of JHP's in my own LCP, and they've fed & fired fine, even in fast-paced drills. They've included W-W STHP & T-Series, Speer GDHP, Rem HPJ/BJHP GS, just to list the ones I can remember off the top of my head.
I prefer to use JHP's in my own LCP. Yes, I know some of the internet experts decry their use for fear of reduced potential penetration that doesn't fall within the 12"-18" range used by one fed agency for determining ballistic performance for duty weapons.
Well, I'm not carrying it as a duty weapon, anticipating using it against multiple armed criminal attackers taking cover behind motor vehicles.
I tend to prefer the possible cutting action offered by a hollowpoint nose cavity, as well as the potential for some deformation or actual expansion, with the wounding characteristics that might involve.
I've seen a couple shootings where .380 ball perforated a clipboard hanging on a wall, the wall next to an outside door behind it, and then hit someone outside the building, in their spine, making them a paraplegic. I've also seen some .380 rounds (I believe they were ball, but it's been a long time since the case) fired into a house. They went through the front window and wall, and as I recall, at least one of the rounds had enough energy to penetrate the back wall of the front room.
Now, .380's are often still approved for use in LE as secondary/off-duty weapons. This can mean having to use whatever ammo is issued, or buying something at their own expense that's approved. It's the skillset and experience of the shooter/user that's arguably of the most importance.
Instead if trying to turn my LCP into a .38 Spl or 9mm ... I'd simply carry a .38 Spl or 9mm (of which I own several of each, BTW).
I'd never think to try ".380 +P", either, as that's not an industry (SAAMI) ammo spec rating, and I'd especially not think to try it in an itty bitty plastic-framed .380 pistol.
I choose my LCP because it can be safely and effectively concealed, in a pocket holster, in the shorter & tighter front jeans pockets in which my 5-shot snubs can't fit. Handy.
I like the little LCP enough that I just bought a stainless version. Why not, since I already own more than half a dozen 5-shot snubs?
If the size of your hands and/or your grip are causing you some issues (thumbing & slowing the slide's cycling), and you can't easily adjust to correct it, perhaps the LCP may not be the ideal choice for your needs. Dunno. Not there to see you use and shoot it.
Just my thoughts.