Halliburton has operated in several oilfield and construction arenas that I have worked in. They are a big, big company, and like any big company they can have many problems. When you are that big it's like being a country, a lot of management at many levels.
In my other life I was an oilfield contractor. I can see how the billing issues arose; they get corrected at audit. Happens a lot, even with government contracts........even small ones.
Very few companies in the world have the degree of experience that Halliburton has, and also the experience in that corner of the world. Actually only a couple come to mind, Brown & Root, Bechtel Corporation and Morrison-Knudsen (which barely exists since Dennis Washington of the Washington Transportation group bought them). It didn't surprise me that Halliburton was considered for the job and awarded the contract; they are capable and qualified. Large contracts, that will be considered cost, plus overhead and profit normally go to a negotiated status after the initial proposals have been reviewed and the contractor's are narrowed down to a most qualified status.
I looked at the website which appears to have severe liberal leanings with ulterior motives. Go talk to them, it will be a camp job in a war zone so your movements may be limited, (meaning it won't be work at a resort in a tourist area, where you can go to town off shift) but it could prove to be rewarding financially and an interesting experience.