What I'd like to do is see if it's possible not only to add on to a posts body/caption (depending on if it's a text or photo post), but alter what may already be there for a reblog. I'm not sure this is possible with the API from what I've tried/seen so far.
For example if the user wanted to delete all previous comments in the caption of a photo post before reblogging it through my system is that feasible with the API? I know you can do it on tumblr normally, but when you pass an argument as a comment for reblog it just adds on to what's already in the posts body or caption.
I guess this is a bit late but I had the same problem and I found the answer after searching for days.
There is an undocumented parameter that you can use in post/reblog or post/edit, 'attach_reblog_tree'. It can be set to true to keep the comments from the original post or false to remove them.
I have to say the last few days were such a waste of time. Such a big site like Tumblr should have this documented. I ended up finding the answer here, in a buried thread on the Tumblr api Google discussion group, which doesn't even show up on Google search.