Oembeds are not embedded correctly in archived site

Please see:
https://wayback.archive-it.org/4739-test/20160509143250/https://dropoutsdropin.org/current-project/

I was able to see a broken stylesheet reference:
https://dropoutsdropin.org/responsive/style.css
and the following do not lead anywhere:
https://dropoutsdropin.org/wp-json/oembed/1.0/embed?url=http%3A%2F%2Fdropoutsdropin.org%2Fcurrent-project%2Fstories%2F&format=xml

https://dropoutsdropin.org/wp-json/oembed/1.0/embed?url=http%3A%2F%2Fdropoutsdropin.org%2Fcurrent-project%2Fstories%2F

So I excluded those 3 URLs from the archive-it crawl scope, but somehow the oembeds end up at the bottom of the page in the archived site.

Any ideas?