I'm not certain I understand the title of your post, vs. the question you ask. What has the FAA to do with the price of tea in China? You're looking for a job with the FAA, or with an employer other than the FAA. If you're looking for work with someone other than the FAA, then the question of the FAA's "relationship with air crew" is irrelevant.
Obviously you will need US certification. How you get that is up to you. You'll need a right to work, and most importantly, you'll need to find someone to hire you.
If you've got low hours (less than several thousand), you may have a tough go finding someone to hire you at the moment. If you have all your certification and you are prepared to apply to entry level positions, regional airlines hire, but they'll be paying in the order of fifteen thousand dollars a year to start. Can you move to the USA and live on that?
If you're looking for positions with US operators abroad, you'll need to be competitive with their requirements. In general, most US operators abroad are flying equipment that will demand considerably more hours and experience than a domestic regional airline will. The competitive minimums, which is really the experience you'll need to compete with others who are qualified to seek the same positions) are substantially higher.
As an example, I fly for a US operator, primarily abroad, outside the US. Our present competitive minimums are substantially higher than the published hiring minimums. To be competitive with others who are getting hired, you'll need in the order of fifteen thousand hours. This happens to be the case because there are plenty of highly experienced aviators who are out of work, and looking.
Don't expect much mileage from being a "fast-mover," especially if you're seeking a corporate or airline position. This isn't to denigrate your experience, and certainly not your skills, but you'll find that a background flying corporate and or airline will be much more beneficial to your quest, than a tactical fighter background. Tac guys tend to have worked hard to get their hours, but they also tend to have low hours, relatively speaking, which gives them somewhat of an uphill battle. I'm sure you've already discovered this.
What type of flying are you seeking, and what are you prepared to do?