Curse you
@Ajax Bay ! I'm partway through the same thing as you!
Mull of Galloway to Kilwinning
Follow Brandane's route as far as Irvine, I can't recommend the Kilmarnock/A77 route. It's just not fun, the cyclepath runs out on the outskirts of Newton Mearns and becomes a crappy cycle lane alongside a busy road all the way into Glasgow City Centre. While Fenwick/Eaglesham Moor can be great, it's not fun getting out there.
It's possible to avoid the A77 and Glasgow entirely by continuing to follow the NCN7 from Irvine north towards Kilwinning.
Kilwinning to Inverness
From Kilwinning your route has two options depending upon your thoughts regarding ferries:
Overland Option
Follow NCN7 from Kilwinning north along quiet roads and old railway paths but leaving the route at Johnstone or Paisley as
@Rasmus suggested and making a bee-line for the Erskine Bridge you can cut out the entire vastly meandering Glasgow loop.
On crossing the Erskine bridge, head west along the route to Dumbarton, from there you have two options to my mind.
- Follow NCN7's mix of off-road routes and minor roads through Balloch, Aberfoyle, Callendar, Aberfeldy and Pitlochry then follow the NCN7 all the way to Inverness. CC Ecosse did this route last year (search the site for writeups on Lochs and Glens North). (My recommendation.)
- Continue west from Dumbarton, through Helensburgh to Arrochar.
At Arrochar you might be tempted by the A82 (don't.), but you should instead go over the Rest and Be Thankful - the old military road. DO NOT follow the main road on the climb!
At the summit, rejoin the main road downhill, follow it round to Inveraray.
You then head for Oban, either by
- Going the (very) long way round Loch Awe on quiet roads and joining NCN78
- Head north out of Inveraray, and be resigned to an unpleasant 10 mile stretch of A85 from Dalmally to Taynuilt.
In either case, there are beautiful back roads from Taynuilt right into Oban. (for route from Oban, see below)
Ferry Option
From Kilwinning follow the signs to Ardrossan, get the ferry to Brodick, round the north of Arran to Lochranza, jump on the ferry to Kintyre and you can head directly north towards Oban and friends via Tarbert/Lochgilphead along NCN78
From Oban there's a cycle route that will take you as far as Ballachulish, then a couple of miles on the A82 before the Corran ferry and the back road to Fort William.
From Fort William your options for getting to Inverness are a bit limited to what NCN78 can offer, the terrain is variable to outright mountain bikey as I understand it. I've encountered plenty of people who have ridden the off-road way to Fort Augustus, and I would not recommend the A82 for love nor money. From Fort Augustus take the quiet but very hilly road to Foyers and into Inverness.
Inverness to John O'Groats
As many options as you want. Roads are significantly quieter north of Inverness - I have cycled on the A9 along there. Wouldn't recommend it though :-)
My preference would be NCN1 from Inverness to Alness, back road to Ardgay/Bonar Bridge, through Lairg, Tongue, Bettyhill and then along the north coast.
Maps
Don't necessarily follow these to the letter, they were pretty hastily sketched out and might contain some dangerous/impassable sections that I or the route builder have missed.
Use them as a jumping off point for your own route plans.
Overland via Pitlochry:
https://ridewithgps.com/routes/12850740
By ferry:
https://ridewithgps.com/routes/12850835