Proof of concept -- loading a basic skeleton for an Angular.js app w/ a userscript on an mTurk target page.

angle-cray-cray.user.js

// ==UserScript==
// @name         Angle Cray Cray
// @namespace    salembeats
// @version      1
// @description  .
// @author       Cuyler Stuwe (salembeats)
// @include      *://worker.mturk.com/?using=AngleCrayCray
// @require      https://cdnjs.cloudflare.com/ajax/libs/angular.js/1.6.9/angular.js
// ==/UserScript==

const globals = {
};

async function main() {

	clearBody();
	showLoadingPage();
	await waitForAngularToLoad();
    clearBody();
	insertAppMarkup();
	insertAppStyles();
    setUpApp();
	manuallyBootstrapApp();
}

async function waitForAngularToLoad() {
	return new Promise((resolve, reject) => {

		let interval = setInterval(() => {
			if(window.angular) {
				clearInterval(interval);
				resolve(angular);
			}
		}, 100);

	});
}

function manuallyBootstrapApp() {
	try {
		angular.bootstrap(document.querySelector(".bootstrapMe"), ['angularApp']);
	}
	catch(err) {
	}
}

function clearBody() {
	document.body.innerHTML = "";
}

function showLoadingPage() {
	document.body.innerHTML += "<p>Loading Angular app...</p>";
}

function insertAppMarkup() {
	document.body.innerHTML += `
        <div class="bootstrapMe"> <!-- The usual way would be to use the ng-app directive, but we're doing it this way here to take control with a manual bootstrap. -->
            <div ng-controller="angularController">
                <p class="success-message">{{ successMessage !== undefined ? successMessage : "If you see this, something went terribly wrong." }}</p>
                Text: <input type="text" ng-model="boundVariable">
            </div>
        </div>
    `;
}

function insertAppStyles() {
	document.body.innerHTML += `
        <style>
            p {
                font-weight: 300;
            }
            .success-message {
                background: green;
                color: white;
                margin-bottom: 10px;
                text-align: center;
            }
            .ng-empty {
                border: 2px solid red;
            }
            .ng-not-empty {
                border: 2px solid green;
            }
        </style>
    `;
}

function setUpApp() {
	var app = angular.module('angularApp', []);
	app.controller('angularController', function($scope, $log) {
		$scope.successMessage = "Angular app successfully started!";
	});
}

main();