I'm currently with employer X and my abstract was accepted to a somewhat prestigious conference very relevant to X. I have an offer from company Y, which is in a completely different industry from X, which I plan to accept, and I'll start my new job before the conference date.
Company Y is unlikely to cover my travel/accommodations. I would like to attend the conference and am ready to pick up the bill. My affiliation on the programme would be Y, which would be almost comical.
I'm thinking there might be value for X to pay for my travel, and I represent X, but this might seem like bad manners if I were to hand in my resignation and at the same time ask for money.
How should I go about this?