Okay, lets look at this, your blowing out bottom brackets, now most bikes come with the cheapest BB the manufacturer can put in there, heck mine was on it's way out, the day I got my bike, it's still on it's way out 2 years later
Now we need to figure out why your destroying this particular component, and several people have eluded to the answer. Your mashing too high a gear, to start and using torque to overcome the resistance. This is hard on components, but even harder on your joints, especially the knee. A 350lb 6'5" guy with bad knees would be scary.
You want to start off in a nice easy gear, on a triple you want to start off on the middle ring, about the middle gear, on a double you want to start off about the second lowest gear on the big ring. This becomes your "home" gear, when ever you need to stop, you want to go back to your home gear as your slowing down. This will take a lot of pressure off the BB, and your knees. As for whether to buy the more expensive or cheaper bike, I would say go with the cheaper one, and upgrade as components break or wear out. Most components, like frame, brakes, headset, fork, front wheel, are not affected much by rider weight (frames are, but most frames are so over engineered that your unlikely to overcome the frame, unless it's one of those high end racing bikes made of pure UnobtainiumŪ).
You want to concentrate your finances on the parts that matter, rear wheel, cranks, BB. BTW stay away from 10 speed components, the chains on those things are really tiny, and expensive, you will probably snap one with the first pedal stroke, You're probably best with an 8 speed cassette and triple crank, giving 24 speeds, the chains on those are cheap and fairly meaty.