Hi Joe - I was looking at various possibilities for you, particularly with views and experiences of the country which you don't really get by plane (unless the Loch Lomond Seaplane that deliberately takes you low over mountains, lochs, beaches- - -)although I guess you have to weigh up the balance of speed/efficiency and also fatigue?!
Some helpful sites are:   travelinescotland which can offer suggestions for your journey options by train/bus/coach/ferry and I think plane as well as walking!
-it is always then best to double check with the rail or bus companies what their actual timetable is also the cost ( eg sometimes local buses are useful for sections of the journey - but they might have anomalies like 'schooldays' or 'school holidays' or certain days only)!
Check the Scotrail website for railcard options - eg the Club 50 costs £15.00 and gives good discounts if you buy online in advance? I am assuming it is open to anyone over 50 not just Scots?!
And - there is a scotrail.co.uk/explore page that enables you to buy special rover tickets that allow you to use(mainly off peak?)for 4 days trains/buses/ferries - including to Northern Ireland - again you would need to investigate which option would be best for you, get you back to Edinburgh in time for Jim's tour.
Maybe some of us could double check your options once you have thought about them, before you finally commit?
As I live in Argyll I checked the Kintyre Express ferry service from Campbeltown to / from Ballycastle - it is a rib with airline seats, takes luggage, covered - not cheap, £50 one way I think - but a brilliant experience! And you might be able to fit in a night in Campbeltown, visit Cadenhead's distillery shop?
Trouble is. they change from their daily service to their end of season weekends-only one the week you arrive! so you'd have to do the Campbeltown to Ballycastle then Belfast (or the other way around) on the Friday/Saturday - and I think only one version gets you to Edinburgh in time?
I need to look at other Campbeltown to Edinburgh options - bus to Glasgow then bus or train Ediburgh or
Bus to Tarbert/ferry to Portavadie / bus to Dunoon (or I pick you up and transport you) then ferry to Gourock / train or bus to Glasgow then Edinburgh or
Rib to Campbeltown Friday late afternoon / Ferry early Saturday am to Ardrossan then train or bus to Glasgow then Edinburgh

Think it is possible to do it the other way around ie bus (plane) to Campbeltown then rib to Ballycastle /bus or train to Belfast back to Scotland via Stena ferry from Belfast (or Larne?) train or bus to Glasgow then Edinburgh
or - fly one of the ways to or from Belfast?
There are some flights from Aberdeen to Belfast - more options from Glasgow/Edinburgh.
The N Ireland travel website is Translink - - - works out journeys tho I advise double checking with the companies?

A few years ago one of my island bagging friends and I did I think at that time it was a 5 day Highland Rover ticket, bus/train/ferry ticket - brilliant! Loads of retired backpackers - amazing!