The weather makes so much difference to what you might want to do. My suggestion is plan nothing for those days after the Haggis Tour, and see how the weather goes.
However I now realise that you have put the Haggis Tour in without marking it clearly. It's the time after the 15th you have to yourselves.
Stonehaven I can see the point of - it has a castle, a fantastic beach, and some highland games, and the rail journey there is very scenic and crosses both the Forth and Tay bridges. The beach is so great as Stonehaven is where the Highland Fault crosses the coast, and I spent many happy hours there with my father many, many years ago.
But I'd knock the London trip on the head. Even though I think you are thinking of using the Sleeper it's a long and tiring trip. I'll point out that early morning is the time for serious beach photography in Stonehaven since it's on the east coast, and sunrise will be somewhere round 5am.
Edinburgh and Glasgow are also stuffed full with all sorts of museums, Edinburgh has the Castle and Holyrood Palace and you can get a tourist bus trip round - check, the ticket was valid all day on as many buses as we wanted when I did that a few years ago. I suspect you can easily spend 2-3 days doing castles, palaces, museums, art galleries and tea-rooms. Glasgow has some very famous ones:
Charles Rennie Mackintosh The Willow Tea Rooms, Glasgow.
Suspect they are very, very busy!