Based on this answer (Linked by @Chocolate in his comment) to a different question, which is much more general and encompasses more situations, here is my attempt at answering myself:
- The causative conjugation 食べさせる means either "make eat" or "let eat".
- While already clear from context, the 〜てもらう reinforces that "let eat" is meant, not "make eat".
- The volitional conjugation 〜もらおう makes the whole thing future-y.
So in the end a more literal translation would be "I shall allow myself to eat", which in context is clearly meant with some irony (/sarcasm? Not sure what the right term is).
I would be thankful if someone could confirm or disagree with this interpretation.