If anyone is interested in a follow-up, I finally got around to asking my Rav about this issue. I won't mention his name, but he's one of the leading Litvish English-speaking Rabbonim in Eretz Yisroel. I asked about who owns the miles now, whether I can ever use them, and whether I can borrow them with the intention of replacing them (via sign-up bonus) if they are needed. His reply is below; in the meantime, the miles still have not been used by the non-Jewish broker who purchased them from the Jewish broker to whom I sold them.
The miles could only be used if they are about to expire OR with the permission of the broker. They are not yours and could only be used when they become zuto shel yam. Replacing them is only an option if they will be available immediately should the non Jewish broker request them.