How to prevent my stacked series from being in reverse order?

You can change order by index parameter which can be set in serie.

http://jsfiddle.net/KLttA/

series: [{
        data: [29.9, 71.5, 106.4, 129.2, 144.0, 176.0, 135.6, 148.5, 216.4, 194.1, 95.6, 54.4],
        index:1
    }, {
        data: [144.0, 176.0, 135.6, 148.5, 216.4, 194.1, 95.6, 54.4, 29.9, 71.5, 106.4, 129.2],
        index:0
    }]

Since this was the top result in google, maybe this saves time for some:

The yAxis has a reversedStacks parameter (since version 3.0.10), which is true by default. To build stacks from bottom up, set this to false. Legend and shared tooltip item order remain correct this way.

http://jsfiddle.net/r5upptLo/

You can use the serie's legendIndex parameter : http://api.highcharts.com/highcharts#series.data.legendIndex