Can anyone help me with this process, especially saving the transposition. Thanks!

There are three areas of transposition, MASTER, KEYBOARD and SONG. When you record SONG in real time you have to use the KEYBOARD area. Be sure to confirm Setup (02:26 sec) before storing the played SONG. Watch a video showing it.
MIDI Song recording - Transpose function

If you want to transpose the channels in a song that’s done, check out this video.

MIDI Song Edit - transpose function on keyboard

Are you looking to transpose just the SMF but NOT your playing, or both?

Thanks guys, I got a handle on it now. I just needed to transpose the SMF not the keyboard.