I've posted an update to the extension I started as a result of this thread: https://inkscape.org/forums/beyond/auto-adjust-fill-colors-to-palette/

https://gitlab.com/inklinea/indexed-colour

I think it's fabulous. 

Just thinkin out loud...

• I'm wondering if it could/should use the active palette as an option, or as an alternative to the external file. 
• In the case of users integrating a new palette into a design, it would be logical for them to install the palette into the user profile and displaying it below the work area... so it would make life easy to be able to use the extension with that or any palette activated below the work area.
• Caveat: I don't know if the active palette is accessible to the API.

I've asked the question of the developers. However I don't think accessing the current palette can be done

It is possible to access all of the items in preferences.xml - but it's not the live version - it's the version which was automatically saved when Inkscape last cleanly exited.

I've got a couple of other ideas though :) Will post if I update.

I've made a slight update to the extension:

It can, use colours from:

- All gradients in document

- Gradients from selected objects

- Gimp palette files

It does not yet use PIL extracted palette from bitmaps.

Euclidean weighting has been added to try to get a better range of colour matches.

It does not at this point recolour  gradients.

I've published the latest update here:

https://inkscape.org/~inklinea/%E2%98%85indexed-colour

No colouring of gradients yet :)