Wow an interesting day for you. Judging by your flight time make sure to online checkin for the SQ flight )

As nishimark says. It's best to drop off your baggage at Osaka station and tour from there.

I would suggest taking the subway Midosuji Umeda station and change at Hommachi and getting off at Osaka port station.

On the way back take the subway to Hommachi station and then from there choose to go south to namba or north back to osaka to retrieve your bags and head to the airport