I agree with the advice not to drive after a transatlantic flight (for everyone's safety not just your own!). Even getting out of Edinburgh airport in a rental car when driving on the unfamiliar side of the road will be hair raising. Indeed I don't enjoy driving to and from that airport and I'm a native.
If you stayed in Edinburgh on the Friday and Saturday evening you'd have a full day in Edinburgh on the Saturday and could then get the train to Inverness on Sunday. Or Saturday evening if timings don't work for a Sunday arrival. Then you could rent a car in Inverness and spend your remaining time driving south via Glencoe.
You obviously don't have lots of time for exploring but you could head south on the quieter east side of Loch Ness, maybe stopping for lunch in Fort Augustus - quite a scenic village on the banks of Loch Ness and with an interesting set of canal locks that help boats tackle a steep descent/ascent.
You could then continue south to Glencoe where there are lots of hiking opportunities (including exploring scenic Glen Etive) before maybe overnighting at the very good Kingshouse hotel at the top of Glencoe on Rannoch Moor. From there you can walk directly on to the West Highland Way (long distance walking route) for a bit, before continuing south by car.
Assuming you have to get back to Edinburgh airport to drop the car and fly out, one route would be to head south on A82, and then at Crianlariach turn left towards Callander on the A85/A84, stopping for lunch in Callander and maybe still have time to see Stirling Castle before heading to Edinburgh.
