My 2c worth -
Take the flight that gets in at night in HKG. Take your luggage. Check in at the Regal Airport Hotel - forgo points for convenience! Otherwise, you can take the train to HKG to Kowloon Hyatt Regency. Rate is around HK$1400 a night - that's about US$180 average.
Take your luggage and leave at checked luggage. It's very tedious to do a go around involving Taipei. Check-in for HKG-TPE-HKG. Leave enough time to return to HKG, go thru immigration and collect your left luggage and then check in again for your Middle East flights.