It leads to what I think is the real goofiboot. I selected the more recent kernel and Solus booted correctly. Thank you!

Here's a higher resolution image of the result of booting from rEFInd:
https://drive.google.com/open?id=0ByCRQBHl_c9ldHdGd2xKRm9TWWc

I tested booting again, for the first time after taking the steps in my last comment. I believe the first attempt is with goofiboot but I'm not sure. The result is shown here: https://youtu.be/IQKwcrQ24Ms

OK, results here. Solus related ones seem to be at the end:
https://gist.github.com/tjgordon/9f90c3a9f012809493919ad3b519c153

The eopkg updgrade works, but clr-boot-manager update still fails in the same way. Log here:
https://gist.github.com/tjgordon/7bfc79cfb32d9270a54306879ef96cf4

I think rEFInd is supposed to update by searching all connected drives each time it starts before it displays the options. I can also try to boot Solus by pressing F10 during boot and selecting it, and the result is the same.
I attempted rescue via chroot as advised at reddit, with result here.