In my experience, most of what you've said above is incorrect. Let me go through and address your question piece by piece. First, do foreign graduates have a hard time getting "kick-ass" engineering jobs at Boeing, GE or Shell? In general no. There are many, many engineers who are on H1B or Green Cards working at companies like these. You'll be limited to non-strategic defense work or work that isn't export controlled, but there are plenty of divisions in GE (Energy, Oil & Gas and Water etc.) and Boeing (Commercial) that are open to non US residents. With regards to oil majors like Shell, I've never heard of a foreign national having trouble getting a job at those companies. Now, let me address the "kick-ass" part. It's my own personal bias, but in general these places are anything but. Large companies tend to get slowed down and fail to innovate due to large amounts of red tape and procedural BS. I read a quote once that, "The long tail of crappy is much larger at small companies." This is true in general also, but if you find one with competent people, working there will beat being at any of the large firms you mentioned any day of the week. Furthermore, many large corporations will treat H1B holders like indentured servants, holding a green card just out of reach. I've seen and heard about it plenty of times. They tell someone they're working on their green card application to their face, all the while dragging their feet behind the scenes, knowing they have the person trapped. Be wary.
Secondly, does a PhD pigeon hole you? Not true either. You're more specialized, but again, there are plenty of PhDs out there working in Business Development, Product Line Management, Technical Sales or General Management.
Next, "end up in O&G (money is there but horrible morally and geographically)." Again, not true. Houston is the O&G hub for the US. Granted it's not Fiji but it's the fourth largest city in the US, has a low cost of living and a moderate climate. There are also plenty of O&G jobs in Southern California, so I'm not sure what exactly you mean by horrible geographically. Morally horrible? Unless you're going to work for a charity, I'd seriously give up on that. There are moral quandaries in any job and let me give you an example. I once worked with a researcher looking at the effects of epilepsy drugs on children to see if they were harming brain development. Pretty morally upright right? Well he had to kill dozens of baby mice every day to extract their brain cells for the studies. Most jobs will have some area that's less than ideal, I hate to sound cynical or jaded, but you need to get over it.
Finally automotive not being cutting edge. Again this is generally false. There is plenty of advanced work going on in terms of electronics, materials and combustion being done at automotive companies. Some of it is being done in the national labs.See also: