So our final itinerary ended up looking like this:
day 1: Arriving. Drive to Stirling.
day 2: Stirling Castle, Wallace Monument, drive to Balmaha (Loch Lomond)
day 3: Hiking around Loch Lomond.
day 4: Hiking around Loch Lomond.
day 5: Drive to Onich (Glen Coe area).
day 6: Hiking around Glen Coe.
day 7: Drive to Portree (Isle of Skye) with a short hike at Glen Nevis along the way.
day 8: Rest day in Portree (Isle of Skye).
day 9: Hiking in the Cuillin Hills (Isle of Skye).
day 10: Drive to Dunvegan, via a long day on the Trotternish peninsula (Isle of Skye).
day 11: Dunvegan Castle and around (Isle of Skye).
day 12: Drive to Aviemore.
day 13: Not really hiking in the Cairngorm National Park (too much rain).
day 14: Drive to Dundee.
day 15: Hiking 'around' Dundee (Glen Clovis, on the southside of the Cairngorm National Park), Glamis Castle.
day 16: Drive to Edingburgh. Exploring Edinburgh.
day 17: Another day in Edingburgh.
day 18: Flying home.
We mostly worked around the weather when it was bad. Had lovely days on the Isle of Skye and around Glen Coe (after an initial grey morning). Aviemore was really the only place where the weather was just too unendingly dismal for us to go hiking.
Thanks again for all the advice here (and through PMs). We didn't manage to follow up on all the suggestions, but that just means we have things to return to Scotland for.