The first automation does not need a phased schedule and a steering committee. Before you start, measure how long the task takes today – for example, by recording the time for a few cases over a week.
In the first week, build the simplest working version. It may not handle every exception – what matters is that it works for typical cases. In the second week, give it to three or four people, note the problems and make fixes.
After two weeks, compare the time with your baseline. If the effect is clear, roll the automation out to the rest of the team. If not, go back to the list from step 1 – the lesson cost two weeks, not six months.