How to copy polar plots to subplots in a new figure?

I have multiple figures with polar plots open, and I'm trying to copy each of them to subplots in a single figure. I cannot figure out how to do this.

This is what I'm currently trying. It throws error "PolarAxes cannot be a child of PolarAxes."

I use similar code to copy Cartesian plots, in which I just use subplot, instead of this polarSubPlot. If I use that when trying to copy a polar plot to the subplot, I instead get error ""PolarAxes cannot be a child of Axes."

What should they be a child of? Is my (new) subplot object wrong, or do I have the wrong object from my existing plot?

figHandles = get(groot, 'Children');
for i=1:length(figHandles)
    hSub = polarSubPlot(rowCount,colCount,i);
    axesPolar = get(figHandles(i),'children');
    copyobj(axesPolar,hSub) %Error: "PolarAxes cannot be a child of PolarAxes."
end

function [polarAxisHandle] = polarSubPlot(rows,columns,index)
    axesHandle(index) = subplot(rows,columns,index);
    polarAxesHandles = polaraxes('Units',axesHandle(index).Units,'Position',axesHandle(index).Position);
    polarAxisHandle = polarAxesHandles(index);
    delete(axesHandle(index));
end