I'm with Chuck on this one your very best bet is to look into a 4 channel interface. Then the process will be very straight forward.
But that said, the next best choice is what you already though of and record in one pass but to two machines.
It would work for shorter songs for sure. I've synced up tracks from 2 digital recordings in the past and around 3 minutes they are fine. So what you could do is start and stop the Yamaha at places between songs.
What you'll want is a very obvious transient to line them up. If there isn't one on the recording, you can always add one if there is room between songs without danger of erasing wanted material. Just record a slap to a mike on Ch 1 and 3
Funny the Yamaha MT100 was my first serious home studio. Used to sync midi using channel 4.
But A new interface would be my first chioce as this is always a welcom addition to any studio.
At the bottom price points here's 3 good ones
The Focusrite 6i6
https://www.sweetwater.com/store/detail/Scarlet6i6G2Tascam us4x4
https://www.sweetwater.com/store/detail/US4X4Pre Sonus 6/8
https://www.sweetwater.com/store/detail/Studio68