@col-klink how about adding to Jill writing (and reading out) that Eustace has invited her to stay for the next school holidays and he's promised to introduce her to his cousins? (...when they go to London for a day trip or whatever...) 
Cross to scene with mother reading the letter aloud (joining in with Jill's voice, then continue with just mother's voice), commenting that she's glad that awful head teacher is gone, and father commenting that she'll probably go and make trouble somewhere else now - probably go into politics! Back to Jill, ending her letter with that she's glad they sent her to this school after all, and signing off. 

It feels like the sort of comedy bit that would work well as a series of mid and post credit sequences.

Inconsequential to the plot, but fun little extras for anyone sticking through the very end 

For what it's worth, the Head's fate in SC seems to be a toned-down version of a rather sharper satirical passage in the "Lefay Fragment", the beginning of a story that Lewis never completed, but that provided some of the basis for MN and a few other elements in the Narnia books:

Once there was a boy called Digory who lived with his Aunt because his father and mother were both dead. His Aunt, whose name was Gertrude, was not at all a nice person. Years ago she had been a schoolmistress and bullied the girls. Then she became a headmistress and bullied the mistresses. Then she became an inspector and bullied headmistresses. Then she went into Parliament and became a Minister of something and bullied everybody.

I don't see the Head's fate in SC as absolutely essential to the story, amusing though it is, so I won't be perturbed if it gets left out of the (hopefully) upcoming Netflix adaptation. The BBC didn't include it in their TV version. But if I were adapting all seven Chronicles, I would include a number of "in-between" bits that we don't see directly in the books — scenes in our world that show the Pevensies and Eustace and Jill and Digory (the Professor) and Polly starting to get together and calling themselves the "Friends of Narnia". Then perhaps in one of those scenes, there could be a brief conversation along these lines between Jill and Eustace — "Oh, did you hear what happened to the old Head of our school?" "Didn't she get made into an Inspector to interfere with other Heads?" "Yes, but it looks like she wasn't much good even at that. I saw her name in the newspaper last week — she's just gone into Parliament." "Oh, well, there's something that'll suit her at last!" (laughter)

That, to me, comes across as a natural way of doing it without being too much of a distraction from the story. I get the "show, don't tell" thing and agree with it in most cases, but occasionally there are times when it doesn't really work. If the film-makers switched to a scene where the Head is now an MP and getting into debates in the House of Commons, that could provide some good laughs for adults if it was written well, but it'd be above the heads of most of the younger viewers, at whom the story is aimed. I'd rather have it left out entirely than done in a way that doesn't suit the overall tone of the story. 

@col-klink    The only way I can think of is to end with Jill writing a letter to her parents explaining what's been happening at Experiment House (minus the Narnia stuff) which we'd hear as voiceover, probably over a montage of the events described. (If they did do that, I think it'd be cute to end the letter and the movie with her telling her parents she'd finally made a friend and for the last shot to be of her and Eustace.)

Much as I can see your point, I'm not really sure from my reading of The Silver Chair's ending that Jill Pole even had parents to write to. That may also explain why, at the beginning of the book, she was bullied at Experiment House. No parents to march in and complain to that Head, about just how their daughter was being treated. Though, having read Earl Spencer's memoir about his own private school education, two decades later, (A very private education), perhaps parents, in UK, weren't always very assertive about looking out for their children's welfare at boarding school, back in those post WW2 days, whilst C.S. Lewis, himself, hated his own pre-WW1 school. 

In the BBC audiotapes, though, the Professor is the narrator and maybe Jill or Eustace might well have written to him or have told him, instead. I'm off to check it out, anyway.  

Posted by: @waggawerewolf27

Much as I can see your point, I'm not really sure from my reading of The Silver Chair's ending that Jill Pole even had parents to write to. That may also explain why, at the beginning of the book, she was bullied at Experiment House. No parents to march in and complain to that Head, about just how their daughter was being treated.

Incidentally — getting slightly off topic — this is my own "headcanon" about Jill, so to speak. We're never told anything at all about her parents or any other family, unlike with all the other child characters. Of course we're not told she is an orphan, but we're not told she isn't either. And just from how alone she seems at the start of SC, it's not a big jump to speculate that she has neither close family nor friends, nobody in her life who really cares about her and has "got her back", as the modern expression goes. That would make it all the more meaningful that Eustace becomes her friend, and all the more wonderful that she finds her way into Narnia. (It also would mean that at the end of LB, there's nobody left seriously grieving for her in this world.)

I think I shared this somewhere a while ago, but if I were directing a new adaptation of SC, I would indicate that Jill is an orphan but not make any big deal of it, let alone turn it into a sub-plot. Just during their initial conversation behind the school gym, when Eustace is telling Jill about what happened to him over the previous school holidays, when she agrees he's completely changed, Eustace could remark "My parents think I've gone completely barmy..." "At least you've got parents!" Jill could cut in, somewhat bitterly, and Eustace, realising this is a sore point with her, tactfully doesn't say anything more about parents and goes back to telling her what happened to change him so drastically. That then just accounts for why we never hear anything about Jill's family, without having to change or detract from anything canonical in the story. 

@courtenay    I think I shared this somewhere a while ago, but if I were directing a new adaptation of SC, I would indicate that Jill is an orphan but not make any big deal of it, let alone turn it into a sub-plot.

Quite so, when there must have been so many ways, especially at the end of WW2, how children could have been orphaned. Though, wherever she was domiciled, when not at school, by LB she was able to join the Girl Guides, where she developed skills that came in good stead during her stay with Eustace & Tirian in a dying Narnia. 

But getting back to Experiment House, I wonder if it was even a boarding school? Or just a forerunner of the Comprehensive School system? 

Posted by: @waggawerewolf27

But getting back to Experiment House, I wonder if it was even a boarding school? Or just a forerunner of the Comprehensive School system? 

It was definitely a boarding school. I'm away from home and don't have the books with me, but although I can't remember whether it's specifically described as a boarding school in the text, it's made clear that Jill and Eustace are stuck there for the entire term with no respite from the bullies. There's no mention of them being able to go home at the end of the day and escape.

Lewis himself was sent to boarding schools from what we would consider an incredibly young age — I can't remember the details, but I'm almost certain he was under 10 when he started. And his first boarding school was the one that was run by an extremely harsh teacher who ended up being diagnosed as insane. So the author himself definitely knew a thing or two about being trapped in such a horrible environment.