You would have to Make the FullModeItemTemplate Like this
<toolkit:ListPicker Name="SourceAccountList" Width="680" FontSize="20" Height="50">
<toolkit:ListPicker.ItemTemplate>
<DataTemplate>
<StackPanel>
<TextBlock Text="{Binding AccountIban}" />
</StackPanel>
</DataTemplate>
</toolkit:ListPicker.ItemTemplate>
<toolkit:ListPicker.FullModeItemTemplate>
<DataTemplate>
<StackPanel>
<TextBlock Text="{Binding AccountIban}" />
</StackPanel>
</DataTemplate>
</toolkit:ListPicker.FullModeItemTemplate>
</toolkit:ListPicker>