Something I did also think of, make sure that you have some form of status as well, for at least the next little while (90 days anyway). If you don't have an OWP or TRP that will be valid that long, you might want to apply for a TRP.
I really hope this works and you can resurrect the dead file. By the wording of the manual, you should be able to, if you tell them that you genuinely thought you submitted enough proof, that you did not get a request for more proof, or a procedural fairness letter.
Keep in mind, that you could, in theory, raise it to a federal court. They would argue that inlands cannot petition the court. But they also have to have a defensible position, that you cannot defeat. If they didn't follow process, or you state they didn't, then you have a reasonable shot at the court instructing them to reopen the file. In that case, it would also mean that you have a reasonable shot at the reconsideration actually working. Don't get your hopes up, just in case, but it's definitely worth the effort now.