About Bottom of my heart, i think there is a confusion.
MJ firstly work on From the bottom of my heart with lots of other singers, in august-september 2005. But, after, in the last months of 2005, he decided to re-write the song, give the production to R Kelly and limit the featurings on the songs to 5 6 singers, including James Brown. They are some articles (on MTV and Rolling stones) which related that.
Maybe Bottom of my heart is this second version. But we have no informations about the first version, "From the bottom of my heart".
Also, i remember an article about the unreleased songs in 2009/2010, and it mentions 2 caricative songs. The first is I have this dream, so the second is likely From the bottom of my heart.
So, in conclusion, i think there are a version of From the bottom of my heart recorded