First, get the job.
Second, apply for advanced parole.
Third, consult an immigration representative, CSR, or even an immigration attorney to see if advanced parole will allow you to travel back and forth. I know for a fact (according to what USCIS has stipulated in the website RE: Advanced Parole) that if you are approved for parole because of employment requirements, you will be able to travel out of the country and re-enter...However, they do not say how often you are able to travel and re-enter, or if you have to apply every time you have to travel.
If I were you, I would first interview and try to get the job. If asked if I could travel or if I need sponsorship, I would say that the immigration situation is personal and in no way will the company have to sponsor me.
My suggestion:
Research the requirements for Advanced Parole...does your employer have to fill out any sections or send any paperwork to USCIS confirming your employment and the need for you to travel?
Can you travel and re-enter on a recurrent basis? if so, how often?
Make sure you have this information on hand before you reach the final round of interviews...if you do, and if the company doesn't have to expose itself significantly if they hire you and train you abroad, you could make a very persuasive argument as to why they should hire and how they could benefit from it...
I wish you much success bud!
On another note, what company is it? Noble, Diamond Offshore, Seacor, Halliburton, Schlumberger, Transocean, Baker Hughes? I asked because I worked for an Oil Trading firm and am well informed in regards to the industry (majored in International Business and Marketing)...
How do they service the industry? Well optimization, testing, drilling, cementing (E&P Sector), Refinery Services/Pipeline Construction (laying) + Maintenance (Downstream/Marketing)? Do they do work Offshore?
For what role are you interviewing?