Not sure what "booked" means. If it's just the flight then you still have some flexibility.
I'd definitely rent a car, as public transportation adds 30-50% to the transit time (with some exceptions). A SatNav or co-pilot with a good map is essential. We use a dashboard GPS that I pre-program with all the routes and stops before leaving the States. One button push first thing each day, with the occasional fiddle for the unexpected.
These suggestions reflect our personal tastes in things to do, but if you get an early start from Edinburgh, you can hit Culloden on the way in to Inverness. Spend just one night in Inverness, then head to Skye maybe via Urquhart Castle and Loch Ness, stopping at Fairy Pools. After night on Skye, do the Totternish Peninsula circumnavigation, maybe with time to hike The Old Man or Quraing. A second night in Skye, then head to Fort William, maybe via Eilean Donan (over-rated). Next day the Jacobite (or diesel) to Mallaig and back. Maybe do Steall Falls or Lochan Trail that evening. Next day, either move on to Stirling or stay another night in Ft. William with some more hiking. If you get an early start from Ft. William, you could see Doune Castle that afternoon (ex-Outlander location), then do the Stirling things (Castle, Wallace Monument, etc.) the next day.
You question isn't clear about whether you're spending the last night in Edinburgh or going from Stirling to the airport.
If you use Google Maps and ask directions between say, Edinburgh and Inverness, then "search for Things to Do" along the route, and populate a travel plan. Add some time to Google driving times (25%?) as they are based on the speed limit, not the speed of sheep, coo, or tractors, nor do they reflect rookie wrong-side drivers. Many sites let you know how long you need to enjoy them, although I think they leave a lot of time for gift shops :-)
You also need to consider how your group travels. You proposal is not very "relaxed" and my changes don't help. It's a bigger country than you think and you might want to consider axing one of your destinations. We're used to "hectic" trips ("We'll sleep in the grave") and our group travels very light (carry-ons) and never unpack. We're at breakfast by 8am and on the road by 9am. And my wife has learned to suppress gasps as we careen down N roads at the speed limit. It wasn't until our third trip that we spent three days in one place (Skye).