I am guessing, but I think it was a long time in preparation. With the UK broad gauge, the difference in gauges was large enough that track could be laid in mixed gauge, so the actual changeover could be years of dual gauge operation. For the Southern US, the gauges were too close to permit mixed gauge, I would think.
An easy way to do a quick change would be to spike the sleepers [US = ties] on one side only left and right on alternate sleepers when laying track to the broader gauge. Gauge would be held by stretcher bars every few sleepers. On changeover day, the stretcher bars could be taken out and the left and right rails complete with sleepers slewed together and the unspiked sides of the sleepers spiked to the new gauge.