Just wanted to follow up on my saga...
The BG2.0 is hands down the must frustrating gun I've ever owned.
I did replace the rear sight with one from a BG380. It definitely narrowed the gaping chasm that the stock sight had and is a little higher to boot which should theoretically help with grouping low, but in reality it didn't. Replacing the sight was a nightmare, I couldn't get a good purchase in my sight pusher so I ended up using a punch set. Wailing on the punch with a mallet alternately did nothing or shoved it way past where I wanted it. I finally got it close enough to try shooting groups, and they were all over the place. At 25 yards I couldn't hit the broad side of a barn, at 15 it was better but my groups were still ragged and low even with a combat hold. I was seriously thinking I'd screwed up in choosing the BG over the Sig 365. Out of frustration, I snapped off two quick shots from low ready at 15 yards.
Both hit more or less POI, well within the A zone of an IPSC target. Easily the best I'd shot the gun, and I'd put basically no thought into aiming. I fired five more two shot groups from low ready, all landed similarly- not the tightest group, but 10 A-zone hits and 2 C-zone, all combat effective hits.
What the hell? It seemed like the less effort I put into shooting the gun, the better I did, the opposite of every other firearm I've ever shot.
I began to notice a pattern- I was firing pretty much as soon as I acquired the front sight, when it was still high in the rear. I was also essentially point shooting using the front sight and ignoring the rear. Are S&W's engineers geniuses for designing a sighting system that counteracts the natural tendency in a stressful situation to snap fire before a proper sight picture is achieved, or are the sights just screwed up in a way that balances out my crappy shooting? Either way, it seems to be working for me. I think I'm ready to declare victory and go home.
As far as ammo, after doing hours of research on .380 ammo I've landed on Winchester "Service Grade" flat nose, pretty much the cheapest brass case .380 you can buy (and as far as I can tell, identical to the Bass Pro/Cabellas Herter brand .380). The general consensus among testers seems to be that flat nose FMJ .380 isn't any worse out of a short barrel than the pricier stuff, especially if you need to penetrate heavy clothing.
The takeaway from all this appears to be don't overthink it.