Am I an entitled little twit?

I say pitch the part time work to the firm as contract. The worst they can say is no which is right back where you are, but if they say yes, between those projects, the other work you are doing, and the start up you have patched together a nice little work stream. A couple of years of that and your network will be so strong that it will probably be a lot easier to find a job, or you won’t need one.