You can embed portal JS forms on any domain
(edit data-ghost attribute value to include your ghost install location)
<script defer src="https://unpkg.com/@tryghost/portal@~0.15.0/umd/portal.min.js" data-ghost="https://yourghostdomain.com"></script>
Portal will then work the same as on your local Ghost site, and you can built HTML forms that post to Ghost in the same way you can in themes.
We plan to create more paths for this in future - but there aren’t many people experimenting with it yet, so it requires some willingness to do some tinkering/exploration