Tumblr’s backup system sucks, but you can do it yourself
The recent changes have caused a fury of backup attempts, in case all posts are deleted on the 19th. The built in backup system is bad. It sets up a downloadable zip (eventually), but that only partially downloads before it errors out, and after 5 attempts I gave up. Wordpress has a system that will import content from another system, but it also stalled for a while and I have no confidence that its going to work.
But worry not, because it can be done without any service! All you need is the patience or knowledge to futz with programming a bit.
bbolli set up a VERY nice beginner friendly script on GitHub to back up an entire tumblr blog. It runs using Python, goes very quickly, and saves to your computer. I just set it to run, and it backed up about 3000 posts and only took 10 min or so. He has some decent instructions on there, so take a look.
https://github.com/bbolli/tumblr-utils/blob/master/tumblr_backup_for_beginners.md
If this looks scary and help is needed, I’ll be paying attention to this post for the next few days and will do what I can.