I've not heard BACK SEAT OF MY CAR from the 'Get Back" sessions yet, but I have a version of ANOTHER DAY from that period. It's very rough, very incomplete and played solo on the piano by Paul. And also a version of HOT AS SUN.
Other 'solo' material that pops up in those January 1969 sessions that I have heard:
LET IT DOWN and HEAR ME LORD, which you know found a home on George's ALL THINGS MUST PASS album.
CHILD OF NATURE... written in India in 1968, John would later rewrite the song as JEALOUS GUY. There's also an acoustic guitar demo of CHILD OF NATURE recorded in May 1968 at George Harrison's house.