Might anyone have any suggestions for saving selected text + images (that is, “web clipping,” as I would define it) from iOS and having it auto-imported into EagleFiler, much like the “EagleFiler: Import” Service does on macOS?
Import from Reading List
Might not fit your use case, but there is an AppleScript to import Reading List items from Safari here.
I generally “clip” the entire webpage to archive rather than just a selection using the following workflow: iOS Safari -> “Add to Reading List” -> [at some point] Switch to Mac -> EagleFiler -> “Import Safari Reading List” AppleScript.
For other snippets, images, files, etc, I save either directly to iCloud drive or to a Pages document and transfer later to EagleFiler.
Not sure about automating the process. You could use a Symlink and dropbox (iCloud drive might not be the best option) to automatically move items into the library (link). You could write an Automator action to open EagleFiler and then automatically run a script–if you open and close EagleFiler everyday then this could take care of some of that housekeeping without explicitly running a script.
Not precisely what you are asking for, but the Importing From iOS page lists some tools and techniques that I have found useful.