The stacking two tickets thing is pretty much a relic of the past now. Your first ticket (local fare) is your Suica/Pasmo card, and your second ticket (express surcharge) can be loaded into the same Suica/Pasmo straight from the smartEX app where you bought your ticket, meaning all you need to do is tap the card once.

It's admittedly a PITA to set up the first time around, but once you've done it, it's silky smooth.