(Since the terminology discussion around Shadow DOM is not making fast progress, my idea is that for now I'll try to write some ideas down in individual issues to later be merged into the specification.)

<script> elements will run when inserted if they have a host-including inclusive ancestor that is a document.

currentScript on document and shadow roots will only point to <script> elements that are descendants and return null otherwise. (Existing scripts expecting currentScript to always be them might have to be updated for this.) An alternative here is that only "closed" shadow roots have an exclusive currentScript and that otherwise both that on the document and of the shadow root work. Given how much properties leak the shadow root already that might be okay too?

Anything else?

Paging @hayatoito @smaug---- @rniwa.