I’ve been waiting for a Tumblr + Bandcamp integration on audio posts since forever and I can confirm that it is working now!
I have no idea when did this happen. I haven’t found any info about this on Tumblr or Bandcamp websites.
Anyway, the important thing is that is working and you can use it by pasting the url of any Bandcamp track into the External URL of the audio post.
This is my track “Glow Dance”, streaming from Bandcamp.