I am the fountain of affection

I'd say no, for two reasons. One is that I always think of "eponymous" as referring to things that are very different from their namesake (example: Frankfurt (a city) is the eponym of frankfurter (a food)). A film and a book are the same thing in different media. Also, the usage is bizarre: "Based on his eponymous 1891 novel" makes it almost sound as if the novel (the antecedent) was somehow planned to have a namesake ("gee, I think I'll write an eponymous novel!"), whereas of course anything is only eponymous after the fact. I'd say it's a case of strained diction from someone who likes the word and forced a fit where "the novel of the same name" would probably have worked better.