BB ammo walks a fine line with high pressures. This is the only way they can achieve their velocity claims. Just like in handloading, running flat out will eventually result in a bad situation.
Its important to remember that the .348" 250 grain bullet does not need hyper velocity to achieve both deep penetration and stopping power. Loads close to 2200 fps work just fine. The price paid by BBA's extra pressures can also easily result in shooting your 71 loose. 50-70fps won't make any difference in the real world.
You can shoot Winchester 200gr. factory loads, which will probably do fine for anything short of big angry beasts, or you can handload.
I've heard good things about Grzzly, but as far as I know, they are still only promising .348 WCF ammo.
