ARM I: Patients receive paclitaxel intravenously (IV) over 60 minutes on days 1, 8, and 15 and carboplatin IV over 30-60 minutes on day 1. Treatment repeats every 21 days for up to 3 courses in the absence of disease progression or unacceptable toxicity. Beginning 4-8 weeks after 3 courses of chemotherapy, patients undergo CRS. Beginning 4-8 weeks after CRS, patients receive paclitaxel IV over 60 minutes on days 1, 8, and 15 and carboplatin intraperitoneally (IP) over 30-60 minutes on day 1. Treatment repeats every 21 days for up to 3 courses in the absence of disease progression or unacceptable toxicity.