If you're connecting in NRT you don't need to go thru immigration - there's a transfer area that puts you into a different security line and dumps you back into the departure terminal.

Assuming you are doing an immediate turnaround at SIN you also don't need to go thru immigration or leave the airport at all. You can stay entirely airside at Changi.

The only immigration/customs you will face is when you arrive back in the US. And if you have Global Entry you won't have to talk to anybody at all!