How long is the discretionary punishment (ta'zir) deserved in a case like this, and am I entitled to determine it?

You have the right to demand qisas (retaliation), or diyah (blood money), or arsh (compensation) if qisas is not possible. As for ta'zir (discretionary punishment) in matters other than the prescribed legal punishments (hudud), it is entrusted to the Sharia judge. You may request from him to imprison your opponent for a period you deem fit, knowing that this matter is subject to the judge's discretion and ijtihaad (independent reasoning).