"QtQuick.PrivateWidgets" plugin "widgetsplugin" not found on static Qt builds using qml MessageDialog

Here's about the simplest sample code I can think of to recreate this issue:

sampleqml.qml

import QtQuick 2.4
import QtQuick.Controls 1.3
import QtQuick.Dialogs 1.1

ApplicationWindow {
    MessageDialog {
        id: errorDialog
        title: qsTr("Sample Message Dialog")
        onAccepted: Qt.quit()
    }
}

main.cpp

#include <QApplication>
#include <QQmlApplicationEngine>
#include <QtQml>

int main(int argc, char *argv[])
{
    QApplication app(argc, argv);

    // Initialize QML
    QQmlApplicationEngine engine(QUrl(QStringLiteral("qrc:/sampleqml.qml")));
    return app.exec();
}

When I try to run this application, I get this error:
QQmlApplicationEngine failed to load component
qrc:/sampleqml.qml:6 Type MessageDialog unavailable
qrc:/QtQuick/Dialogs/WidgetMessageDialog.qml:42 module "QtQuick.PrivateWidgets" plugin "widgetsplugin" not found

This ONLY happens when I compile it against a statically built Qt. My qtquickcontrols module IS installed (as far as I can tell...). I've even tried to make it specifically using "make module-qtquickcontrols".

Here's a list of my Qml libs in my installed lib directory (I'm pretty sure I have them all, but here's a few just to rule that possibility out):

libQt5QuickParticles.a
libQt5QuickParticles.la
libQt5QuickParticles.prl
libQt5Quick.prl
libQt5QuickTest.a
libQt5QuickTest.la
libQt5QuickTest.prl
libQt5QuickWidgets.a
libQt5Widgets.a
libQt5QuickWidgets.la
libQt5Widgets.la
libQt5QuickWidgets.prl
libQt5Qml.a
libQt5QmlDevTools.a
libQt5QmlDevTools.la
libQt5QmlDevTools.prl
libQt5Qml.la
libQt5Qml.prl
libQt5Quick.a
libQt5Quick.la

My workaround is to... simply not use MessageDialog at all. All my other QML items appear to work (I haven't tried EVERY Qt Quick Controls item, but I have used quite a bit of QML, and this was the only error spot).

The other workaround is to build Qt as a shared library.