Arguably the value in potential change of the rich interacting with the poor is immeasurably higher than the meal itself's monetary value.

I think if I needed to do this in a UK community where I wasn't already known then I'd speak to a MP/councillor and say I wanted to fund them having a meal with X poor families so they could hear about their struggles and such.

It's actually an interesting challenge.

You could probably donate '5 family pizza dinners' to a school in a poorer area, eg for a school fair.