Yeah i had the same problem while testing around with 5.3.2 glad you can confirm this for newer firmware, too. I'm also using a let's encrypt certificate that is
not known by the WiiU. I think the package can handle https-requests but maybe not https-requests for unknown certificates (5.3.2 can).
@Kafluke you should consider that when doing your tests. I've fixed it the same way you did, by using a subdomain. I thought i have also fixed the problem then but i have to retest it, maybe we can then fix the 5.5.1 the same way, too. By the way, is your hoster "all-inkl.com"?
Edit1: As i have already suspected, https (let's encrypt certificate) + 5.3.2 is working for me. There are only 2 ways i've could fixed that. Either the minibuffering function or the remove of the menu.json/javascripts.
So the question is - did you have tested your hosting with the mp4 files or the index.php - or both? If you've only tested with the mp4 files, try the index.php because they are buffering the mp4 files first.
https://yourserver/hbl/index.php
Edit2:
@Kafluke If you need a webspace to test (including https let's encrypt certificate) i can give you a ftp-user to my hosting.