Nintendo Switch game saves can't transfer between systems
You'll have to finish 'Legend of Zelda' on one machine.
It's not just your Nintendo Account that latches on to one Switch at a time -- your game saves are stuck, too. Nintendo has quietly posted word that saves are stored exclusively to the console's built-in storage, so you can't just transfer your progress to another system like you could (however awkwardly) with the Wii U or 3DS. If you're determined to complete Legend of Zelda, you'll have to finish it on the system where you started.
Will this change? The answer is a resounding "maybe." Nintendo confirmed to Kotaku that you can't transfer saves "at this time," which leaves the door open to an upgrade but is far from a guarantee. Either way, this isn't very thrilling news if you're coming from virtually any other console... particularly a PS4 or Xbox One, where cloud saves are within easy reach.