Have you tried calling the lawyer and telling them the date is no good but "X" date would be fine?
Or, (and I freely admit a lack of knowledge as to FL civ pro), but I only use a subpoena "deuces tecum" to obtain documents (and I put a big "No personal appearance required" disclaimer at the bottom). So there's a chance they only want the paperwork and not your appearance, which might make the deadline easier to live with.