I'm not from Scotland but I'm close by being in Newcastle. I can tell you that the shuttle train service between Edinburgh Waverley and Glasgow Queen St takes 50 mins however if it was me I would stay in Glasgow. From the last three gigs I went to at Hampen Park the show finished between 10:30 and 11:00pm. Due to the amount of people getting a train from the nearest station (Mount Florida) was an impossibility and it was either a 2-3 mile walk into the city centre or walk to the next station up the line and take pot luck.

I would say by the time you get back into Glasgow City Centre it would be too late for a train back to Edinburgh. However whether there is a night bus I don't know.