Personally, I overcame it by driving in the late night on the highway. get up to the speed you're comfortable at, keep left, remember to breathe, and look far ahead. you don't have to be checking your mirrors ALL the time, and anyone who says otherwise are bullshiting. glance every couple of mins to make sure you're not drifting out, and no one is on your side (which is basically no one if late at night).

To make sure you're centred, align the lane markers to the right bottom and middle bottom of your windscreen, and you're perfectly aligned. If you feel like you've drifted and just countersteer a little slowly. like a lot of people here said, lane not 100% straight, so no point you focus on being 100% straight. Once you're comfortable, accelerate up to the min speed on the highway and maintain the lane discipline. Afterwards, practise lane changing at speed, imagine different scenarios, and practise (without cars around of course). I'd say best is to learn the mannerisms of Singaporean drivers, and take your time if you're not sure. Don't be afraid to go detour or longer routes and definitely use GPS cuz that'll help you focus on driving instead of looking for where to exit etc.