Severance pay and salary: "double dipping"?

My company was recently sold, and I was laid off with no notice. However, my final check included two weeks salary that was designated as "severance pay". During the following two weeks, I continued working voluntarily to finish up a very important project which had been pending at the time of my layoff. I was under no obligation (contractual or otherwise), but did this mainly out of loyalty to my fellow employees. After another week had passed, the new company owners, evidently impressed with my work ethic in this situation, offered me a job. When I asked about receiving compensation for the work performed after my layoff, they claimed that the severance pay from the previous owner should cover it. I contend that "severance pay" has nothing to do with this, that I would have received it regardless if I had done any additional work or not. I've suggested to them that they either make my effective re-employment date the day I was laid off by the old owners, or pay me as an independant contractor for the work performed. They've rejected both these proposals as, in their words, "double dipping". I don't want to poison my relations with this new company, but I think it's fair that I be paid for the work I did. How can I best convince them of this? Thank you.