Can you not do a big 'horseshoe' on Map IS, Glasgow-Stirling-Edinburgh-Aberdeen-Inverness? That would avoid Perth.
A part of me thinks that under normal circumstances you'd have to change at Larbert and Haymarket to avoid doubling back on yourself...
However, from experience, I've often found it cheaper to but a rail ticket from Glasgow Queen Street to London (change at Stirling) onto the Highland Chieftan than to buy a ticket direct from Stirling on the HC.
There is also the potential to route via the only daily train from Glasgow to Fife...
17.33 Service Glasgow Queen St to Kirkcaldy, arriving 19.05
20.10 Service Kirkcaldy to Inverness, arriving 23.14
This won't take you via Aberdeen, but will take you over 1 of the least used passenger routes in Scotland