[PubQ] Publisher hasn’t paid me for a short story, even after the collection was published

I sold a short story to a publisher to be part of a collection that was released a few weeks ago. I signed the contract back in January, and it says I was to be paid my advance by March 1st, but I still haven’t been paid.

I’ve reached out constantly (like every 1-2 weeks) since then, both to the person who I was in contact with about acquiring the story, and the person who handled the contract paperwork. They keep saying it’s an error on their end, and I absolutely should’ve been paid, and they’re going to fix it right away. But then they never actually do. I’m getting pretty frustrated, especially now that the collection is officially published.

They’ve sent me promo materials for the release, so I know they have my correct address (and I include it every time I email them). They’re also a pretty big reputable publisher, and I can’t find any lawsuits or similar situations online about them.

At this point, is my best bet small claims? I really don’t want to have legal action against a sizable publisher or burn any bridges, especially when I’m about to be on submission with a novel. Do I just suck it up and accept I’m probably not going to get paid?