I don't think spending 7 - 8 hours is a fantastic idea, even with lounge passes.

Grab (the SE Asian equivalent of Uber) does typically offer better rates than taxis. Especially if it's just one person. You can choose the Grab Share option which will take longer than a direct Grab, but will be $2-3 cheaper. I would add 50% to the expected travel time. So if it takes 30mins from city centre, allow for 45 minutes.

For the 9 am flight, you would want to get to the airport around 7.30, so booking a grab at 6am should get you there in time - at least you get some kip in a bed (that you've paid for) rather than in a lounge.