How can I define a GridView for a WPF ListView so that the ListView items are distributed over more than one column?

Question

I have a data-bound ListView in WPF with the ListView items being rendered as RadioButtons. I want to use a GridView to display these in a grid. I can find numerous examples for using a GridView where the data is to be displayed in columns (with different item properties in each column) but I want an entire child item in each cell not the rendering of a specific property.

In other words, I'd like something like this:

    <ListView ItemsSource="{Binding OptionItems}">
        <ListView.View>
            <GridView>
                <GridViewColumn>
                    <GridViewColumn.CellTemplate>
                        <DataTemplate>
                            <RadioButton
                                Content="{Binding Option.Value}"
                                IsChecked="{Binding IsChecked}" />
                        </DataTemplate>
                    </GridViewColumn.CellTemplate>
                </GridViewColumn>
            </GridView>
        </ListView.View>
    </ListView>

but with the column repeated, with the desired result that the items spread evenly three (or however many I set) to a row.

Is there a way of doing this? Is a GridView even the correct way of trying?

I currently have the items displayed using an ItemsControl and a WrapPanel but this isn't spacing the columns evenly and, despite much tweaking, isn't achieving the correct effect.

I have thought of achieving this by having a contrived property in my ViewModel that collects the items into groups of three (or however many I set) and then showing each sub-item from within the group in each column but that does seem a very ugly solution.