Academic affiliation: which to choose?
My immediate reaction is to put them both on; It is not unusual to have two affiliations. I then mean to state "A and B" to show a shared affiliation. That way both departments could benefit from your publication. The question is then how to get the different departments to losen up their purses. In my system no such funding is typically given out by departments/university, one has to apply for money from different sources oneself. I could possibly convince my head to provide the money if the reason was particularly well deserving. So I cannot comment on how such support would be provided.

I would suggest communicationg with both univesities stating that you will publish the paper with them as an affiliation to see if anyone would provide funding. I would obviously put any funding source as my first affiliation afte the fact.

Finally, to get a request to put an extra name on the paper in order to get money sounds terrible, in fact unethical. It is of course easy to say that when you are not facing the situation so thumbs up for standing up to that behaviour.