The company overall is quite stingy and I doubt that they will do this part. I'm trying to figure out what other things that I can ask for other than financial compensation. Someone mentioned Promotion and a positive review is something to ask for, which makes some sense. The only problem is according to my review, I'm already exceeding expectations. So, this project doesn't buy me much.
Overall, they are fine, and kind of, want me to drive the project, essentially because there is no one else who can do that job.