In addition to the downsides you've already heard about the .380 have you considered price & availability of ammo. I haven't seen any locally for about 2-3 months. On line sources say they won't have any until June or July in most cases if, they speculate at all.
These caliber guns are being heavily marketed in proportion to the increase of CCW permits being handed out. You would seem to be the typical buyer in that you just want something you can throw in your pocket and not have to think about concealing it any further.
Whatever your decision I wish you good luck with it.
P.S. Were you able to try the LCP at the range? You may be surprised at your ability to manage recoil.