They will know you spent a small amount of time, because your champion has championned you as being able to solve the problem, not "having a ready made solution".
They won't be able to ship, but unfortunately, they don't know it yet. They might fear it, but the management probably won't admit it, because if they did, they wouldn't have set themselves in this trap in the first place...
The $250hr vs $25k makes think of an anecdote about Picasso (found no credible source online about it, sorry): During an event, he scribbled a figure on a napkin. The napkin was instanly worth serious $$$. "This will pay for my dinner" he said. The restaurant manager objected, saying "But it only took a few seconds to draw this!". No, he said, it took me my whole life.
I don't know if it's apocryphical or not, but I try to keep that in mind.