I probably faced the same problem as you with version 0.6.3. I found 2 bugs:
(1) All images are imported but the links to a few images are not modified in the uploaded version of the text. In those cases, the image displayed is the very one stored on the old site, even though it is also present in the media of the new site. This is very bad because these images will disappear as soons as the old site has been trashed!
A workaround is to modify the URLs of all pictures. For instance, I used a search-replace plugin to change:
lebonheurestpossible.files.wordpress.com
to
lebonheurestpossible.org/wp-content/uploads
It worked fine, but bug #2 turned up…
(2) When importing images, the plugin messes up their “dates”. For instance, I had an image whose source was:
src=”https://lebonheurestpossible.files.wordpress.com/2015/08/time_is_a_changin.jpg?w=300″
After importing it became:
src=”https://lebonheurestpossible.org/wp-content/uploads/2015/12/time_is_a_changin.jpg?w=300″
So, changing the beginning of the URL as shown in (1) is not sufficient. I needed to fix all wrong picture URLs by hand!
I believe that instead of picking up the creation date of the image (as WordPress presumably does by default), the import plugin used the date at which the image has been imported to the old site. Or something of the kind. Programmers should be able to figure out and fix it!
Except for this (very troublesome) problem, the plugin worked perfectly for the transfer of my site. At last, no 504 error! It took time, indeed, but that’s the time needed by the host of the new site to download files from the old site…