G'day Again!
Ok, so found a better fudge, though still a fudge rather than a fix.
I opened the json file in ArcGIS Online Assistant
There is a section for the timeSlider widget.
I added the currentTimeExtent to match my startTime and all now appears to work as I need.
"widgets": {
"timeSlider": {
"properties": {
"startTime": 1372636800000,
"endTime": 1467331260000,
"thumbCount": 2,
"thumbMovingRate": 2000,
"currentTimeExtent": [
1372636800000,
1372636800000
],
"timeStopInterval": {
"interval": 1,
"units": "esriTimeUnitsYears"
}
}
}
},
Enjoy