From Inverness back to Edinburgh or London coin toss

From what airport will you depart for home?

Will you have a car?

You could take a ferry or flight up to the Orkney Islands. You could take a short detour to visit the Lake District for a few days stopping at Hadrian's Wall.

If you are not on an open jaw ticket and flying back from London, rather than Edinburgh where you presumably landed it seems a huge diversion to go down to London for a few days.
There is far more of Scotland to see, you could even fly or ferry up to the Shetland Isles.
But there is much of interest in Eastern Scotland, the Borders, South West Scotland and the Clyde.
For unknown reasons most people's geography seems to end at the Orkneys but Shetland is just as full of history and glorious scenery.

There's also much to see in the Hebrides.

People forget to mention those.

Hebrides, yes. Any specific suggestions beyond where we are
already going in the Hebrides?

Yes on having a rental car from Glasgow. And no, haven't purchased flight tickets yet or most of our overnight stays. Flying into Edinburgh and not needing to fly home from there necessarily. It's the last end of the trip from Inverness (3 days remaining) we are trying to figure.

Thank you all for your suggestions, we are considering everyone's :)

If you’ve never been to London, I would absolutely add the last three days there and fly home from there. You can even do an overnight train from Scotland to England to save time and hotel costs. Www.sleeper.scot

What about the North Coast 500? You're already driving part of it, just continue around to Inverness. This would be adding the three days before Inveress.

https://www.northcoast500.com/

You are only just touching the Inner Hebrides.
There is the whole outer Hebrides- fly into the beach landing strip on the Isle of
Barra.
Ferry to Eriskay.
Drive over to South and North Uist, and Berneray. Ferry over to the combined Isle of Lewis and Harris.
From Stornoway Lewis fly back to Inverness or other airports. Or ferry to Ullapool for the NC500.
From North Uist or Harris ferry to Uig on Skye.
Or of course from Skye do it the other way round.
I haven't even mentioned the many other isles to explore in the Inner Hebrides.
Or in the Clyde Estuary and from Kintyre, including Islay and remote Jura.
Driving on the mainland there is also the NE250, the SC300.

You haven't touched Mull and Iona either.

I think you're moving awfully fast those first 10 days and would slow down the itinerary. Skye's a good place to spend three full days, just as one example.

Keep in mind that western Scotland is very wet. You could be uncommonly lucky, or you could have multiple days on which significant outdoor activities don't seem all that attractive.

Accommodation on Skye in particular will be very hard to find assuming you are talking about June this year and not next. Your best bet might be the Skye Rooms facebook group that aims to match providers with availability to those seeking last minute stays.

In terms of your extra days, I'd be tempted to slow the pace of your trip and spend more time in each spot. But you could also consider the islands of Mull or Arran, or a trip up to the Orkney Islands. If you want to visit islands other than Skye you will also need to book ferries and availability might be an issue this close to June.