Lochcarron to Ullapool 68 miles.
I guess a 'fair chunk' is subjective.
It's a wee bit more than 68 miles if you take the coastal route via Gairloch and Torridon.
Incidentally that part of the route which is on the A832 is known as the Destitution Road. By the 1840s the highland population had become dependant on the potato as a staple of their diet and just as in Ireland successive crop failures due to potato blight led to widespread famine. Various relief rations were available mostly in return for labour. Around 1848 the government introduced the so called “destitution test” whereby men had to work for a minimum eight hours a day, six days a week, in return for their meagre oatmeal rations. They were employed on various public works including road building.
The road between Braemore and Gairloch is one of the most well known of the destitution roads and is well worth doing. I cycled it some years ago as part of a tour of the Hebrides and west coast of Scotland, very similar to Matt's route. It begins by climbing the Corrieshalloch Gorge before crossing remote moorland surrounded by distant peaks and descending through woodland to the shores of Little Loch Broome. It then mostly follows the coast, including Gruinard Bay and the offshore Gruinard Island, location of the infamous WW2 anthrax experiments.