What i did is, when i was in Mainland China server, i pressed the gateway button for 5 seconds in order to reset it, then i logged in Singapore server and did a manual scan without success. I then noticed that the yellow flashing in Gateway had stopped so i took it out of ac power, plugged it in again and did a reset AGAIN.
Then i logged in back to mainland china and directly logged in back to Singapore server and when i pressed the manual addition it found the Gateway right away.
I could find it that way (following the same steps) about 8 days ago when i tried again but back then i couldnt finish the installation process as i already said (it timed out) this time it worked perfectly.
The time out (that you mention) happened with the PREVIOUS firmware of the gateway. Since then i received an update to the firmware and this time the process finished without problems.
The gateway is initializing, every sensor works, every bulb works and alexa works. I can turn my lamps on/off from the wireless buttons, have automation and have alexa with yeelight at the same time.
Be careful to have the same firmware in the gateway and the same version of Mi Home as me.
Have in mind that with the latest firmware the gateway is now called "Mi Control Hub" and in Child devices you can find the aqara wireless switches.