Hi Paige -
Here are a couple of thoughts.
In the time you have the ‘slow travel’ will of necessity take a back seat, because you are covering a lot of ground in a comparatively short time.
This is one of the best cases ever for an open jaw flight booking. Either fly into Glasgow/Edinburgh and leave from Paris or vice versa. Personally I would fly into Paris, spend a few days there, then take the high speed train to London and spend some time there and then travel on by train (or plane) to Edinburgh. The train will show you more of England going up the east coast so may fit in better with your slow travel. I’d be inclined to spend roughly the same amount of time in each location - even then, you won’t be able to do it all, but this isn’t a criticism of the planned itinerary, it’s just the observation that there’s a lot to see and do.
On your schedule, I wouldn’t go to Skye. It’s still quite a trek from Edinburgh and you’d be coming back almost immediately you arrive, and you’d severely eat into your time in Edinburgh. Skye is a big island and takes a while to cover anything like thoroughly. Because of this, I see Skye as a destination in its own right and I’m a bit concerned by the reports that suggest it has been overrun with tourists in recent times, making accommodation potentially difficult. From the reports and videos I’ve seen most don’t visit the places I think are best on Skye, and here I’m referring to the Cuillins. That said, these are particularly rugged mountains and not for the casual or inexperienced or poorly equipped and it is my personal preference. If you are determined to see Skye I would book on a Rabbies tour (or similar, other tours are available) mainly because, yes, to see Scotland best you really do need a car. Where a car is as much use as a chocolate teapot would be central Edinburgh though!
I’m sure you’ll get more detailed responses here and plenty that will tell you that you are biting off more than you can possibly chew in the time available. But that said, it’s your trip and if it’s what you want to do then go for it. You’ll see plenty, but certainly not everything and you may find you are travelling a bit more ‘intensively’ than you planned. I hope you have a great time!
Ian