Thanks - the cheapest non-railcard Advanced 1st Class Ticket I can find between Edinburgh and Inverness is £45 on Scotrail on the dates I want to go - do they get any cheaper than that ?
You can upgrade to 1st class on IC7 services for £15 one-way on weekdays and £10 on weekends.
However it's not clear if it's possible to upgrade Standard class advance tickets.
The ScotRail site doesn't mention an exclusion, but that's not to say it doesn't exist.
https://www.scotrail.co.uk/tickets/first-class