Of course they're in it for the money, this is their livelihoods. With that said, I hope Omega doesn't continue to fight the decision after this first go round, but we're also talking about vast sums of money, so I'm not holding my breath. Also, I'm sure they've invested a lot of time and money into their planes and business over the years, so I'm sure they're not just going to walk away without a fight. Also, maybe they're trying to buy time as well with a hope that TMPS will offer a subcontract. Personally, I think this will get resolved sooner rather than later. Maybe that's just me being optimistic, but like you eluded to, this isn't a contract to build a warehouse or something, this contract is on a much higher level, so I'm hoping the decision making will be swift.
Protesting to the contracting officer instead of directly to the GAO has some advantages. The company protesting can often gain additional time to gather more information that will assist it if it later protests to another forum.
If their next step is to bypass the contracting officer and they file their protest directly with the GAO, this is the end of the line for their protest. The GAO's decision is final, and you cannot appeal it anywhere.
In the past, some companies would protest every contract that they lost, which can create an adversarial relationship that can work against you on current or future contracts. If you are going to protest, you must have a "real" reason (vs. just sour grapes) and you must have evidence to back up your claim. I think Omega's protest is flimsy at best.