So East Coast would not run from Edinburgh to Glasgow via any alternative routes?
The normal route is via Carstairs
However they used to run via Shotts (HST), if necessary and had already been planned, otherwise not run at all between Edinburgh and Glasgow (Class 91)
Before I worked at InterCity East Coast, a HST got trapped at Glasgow QS (around 1989), having worked the morning Edinburgh - Glasgow QS, to then work the Glasgow QS - Kings Cross
The line had become blocked at Winchburgh, and the other ScotRail Express sets were running a shuttle service between Falkirk High and Glasgow QS
However the HST had to travel to Perth, Ladybank (at the time unused for passenger services), and Forth Bridge
Apparently it caused some confusion at Perth as it arrived from the south, the station staff were expecting the Inverness service approaching from the north!