GridLayout and Row/Column Span Woe

The Android Developers Blog post introducing GridLayout shows this diagram of how spans impact automatic index allocation:

I am attempting to actually implement that using a GridLayout. Here is what I have so far:

<android.support.v7.widget.GridLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res/com.commonsware.android.gridlayout"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent"
    app:orientation="horizontal"
    app:columnCount="8">

    <Button
        app:layout_columnSpan="2"
        app:layout_rowSpan="2"
        android:layout_gravity="fill_horizontal"
        android:text="@string/string_1"/>

  <Button
    app:layout_columnSpan="2"
    android:layout_gravity="fill_horizontal"
    android:text="@string/string_2"/>

  <Button
    app:layout_rowSpan="4"
    android:text="@string/string_3"/>

  <Button
    app:layout_columnSpan="3"
    app:layout_rowSpan="2"
    android:layout_gravity="fill_horizontal"
    android:text="@string/string_4"/>

  <Button
    app:layout_columnSpan="3"
    android:layout_gravity="fill_horizontal"
    android:text="@string/string_5"/>

  <Button
    app:layout_columnSpan="2"
    android:layout_gravity="fill_horizontal"
    android:text="@string/string_6"/>

  <android.support.v7.widget.Space
    app:layout_column="0"
    android:layout_width="36dp"
    />

  <android.support.v7.widget.Space
    android:layout_width="36dp"
    />

  <android.support.v7.widget.Space
    android:layout_width="36dp"
    />

  <android.support.v7.widget.Space
    android:layout_width="36dp"
    />

  <android.support.v7.widget.Space
    android:layout_width="36dp"
    />

  <android.support.v7.widget.Space
    android:layout_width="36dp"
    />

  <android.support.v7.widget.Space
    android:layout_width="36dp"
    />

  <android.support.v7.widget.Space
    android:layout_width="36dp"
    />

</android.support.v7.widget.GridLayout>

I had to introduce the <Space> elements to ensure each column had a minimum width, otherwise, I would have a bunch of zero-width columns.

However, even with them, I get this:

Notably:

• Despite android:layout_gravity="fill_horizontal", my widgets with column spans do not fill the spanned columns

• Despite the android:layout_rowSpan values, nothing spans rows

Can anyone reproduce the diagram from the blog post using a GridLayout?

Thanks!