Hi.I do a lot of this work. I mostly have tracks I made myself but now I'm lazy and if I find a good download I'll use it. I make a lot of backing tracks for my solo act and a Duo I play in. I mostly want bass and drums.
Like you I start with the TTS-1 which wil play the song the way it was composed. You need to OPEN the file to get the correct parameters.
I then insert Addictive drums and the SI bass for starters and re assign those tracks.
With addictive drums you can change it to play GM sounds- Go to the ? in uper right and / Maps. Or you can drag the "part" to the proper note value that AD uses. Tricky with the hI hat.
And yes you often find percussion sounds missing so what I do is clone the channel 10 midi track so I have 2.
I then highlight and delete parts so that one track contains only parts for the TTS-1 and the other the parts to be played by AD.
SI Bass might require transposing +12.
From there I might use better organs and piano etc. Lots of choices.