This script adds a new sticky header to Basecamp projects and todo lists on scroll.

basecamp-projects-sticky-header.user.js

// ==UserScript==
// @name         Basecamp - Projects Sticky Header
// @namespace    http://tampermonkey.net/
// @version      0.13
// @description  This script adds a new sticky header to Basecamp projects and todo lists on scroll. Never forget where you are again!
// @updateURL    https://gist.github.com/lucaswilric/75f9492fc64befed433e32b3013bc1ab/raw/basecamp-projects-sticky-header.user.js
// @downloadURL  https://gist.github.com/lucaswilric/75f9492fc64befed433e32b3013bc1ab/raw/basecamp-projects-sticky-header.user.js
// @author       Dan Berkowitz, Lucas Wilson-Richter
// @match        https://3.basecamp.com/*
// @grant        GM_addStyle
// @require      https://npmcdn.com/headroom.js/dist/headroom.min.js
// ==/UserScript==

GM_addStyle(
	'#project-header-clone { pointer-events: none; transition: transform 120ms ease-in-out; font-size:0.9em; position:fixed; top:0; left:0; right:0; transform:translateY(19%); z-index:-1;}'
);

GM_addStyle(
	'#project-header-clone:not(.headroom--top).sticky-pinned {transform:translateY(120%);}'
);

GM_addStyle(
	'#project-header-clone.project-header-mobile__padding-top-bottom, #project-header-clone.project-guide__header { display:none; }'
);

GM_addStyle (
	'.sticky-pinned h1 > span.options-menu { background-color:var(--color-bg--main); padding:.5em; box-shadow: 0 1px 3px 0 rgba(0,0,0,0.4); border-radius: 0 0 0.6rem 0.6rem;}'
);

GM_addStyle (
    '#project-header-clone button.recording-breadcrumb__jump, #project-header-clone span.recording-breadcrumb__jump-menu {display:none;}'
);

GM_addStyle (
    '.nav__main { background-color:var(--color-bg--main); max-width:100%; width:100%;'
);

GM_addStyle (
    '#project-header-clone .crumb-wrapper { pointer-events: all; display:inline-block; background-color:var(--color-bg--main); padding:.5em; box-shadow: 0 1px 3px 0 rgba(0,0,0,0.4); border-radius: 0 0 0.6rem 0.6rem;}'
);

function scrollToTop(scrollDuration) {
    var cosParameter = window.scrollY / 2,
        scrollCount = 0,
        oldTimestamp = performance.now();
    function step (newTimestamp) {
        scrollCount += Math.PI / (scrollDuration / (newTimestamp - oldTimestamp));
        if (scrollCount >= Math.PI) window.scrollTo(0, 0);
        if (window.scrollY === 0) return;
        window.scrollTo(0, Math.round(cosParameter + cosParameter * Math.cos(scrollCount)));
        oldTimestamp = newTimestamp;
        window.requestAnimationFrame(step);
    }
    window.requestAnimationFrame(step);
}

function cloneHeader() {
	var projectHeader = document.querySelector("div.recording-breadcrumb__title");
	var mainNav = document.querySelector("ul.nav__main");
	var clone = projectHeader.cloneNode(true); //Clone the projectHeader DOM node and all child elements

	clone.id = "project-header-clone"; //Add an ID tag to the cloned node so I can target it individually.
	mainNav.appendChild(clone); //Append the cloned node as a child of mainNav

    // The breadcrumbs don't have a wrapper, so we need to add one to style them. We can also enhance the breadcrumbs by getting the task name from the window title and appending it
	var modified_HTML = "<div class='crumb-wrapper'><a class='scrollTop' style='cursor:pointer;'>⬆</>" + clone.innerHTML + '<div class="recording-breadcrumb__separator" style="display:inline;" aria-hidden="true"> › </div>' + document.title + "</div>"; //Copy the breadcrumb nodes from inside the cloned element, get the page title (which is the task name), and then wrap them in a div
	clone.innerHTML = modified_HTML; //Replace the cloned element's inner HTML with the newly wrapped nodes

    // Add ability to scroll to top of page.
    let scrollTopButton = document.querySelector('.scrollTop');
    scrollTopButton.addEventListener('click', function(){
        scrollToTop(200);
    });
}

function makeSticky(x) {
	var headroomJS = new Headroom(x, {
		"offset" : 200,
		"tolerance" : 0,
		"classes" : {
			"initial" : "sticky-top",
			"pinned" : "sticky-pinned",
		}
	});
	
	headroomJS.init(); //Initialize Headroom.JS
}

document.addEventListener("turbolinks:load", function() { // Hooks into Turbolinks' page load event (https://github.com/turbolinks/turbolinks#full-list-of-events)
	var cloneExists = document.querySelector("#project-header-clone");
	if ( cloneExists === null ) { // If element does not exist
        	cloneHeader(); // Clone and append the element
        	cloneExists = document.querySelector("#project-header-clone"); // After clone and append, redefine cloneExists variable in the local scope
	}
	else {
		cloneExists.remove(); // Remove the cloned header due to it persisting for one page too long
		cloneHeader(); // Clone and append the element
		cloneExists = document.querySelector("#project-header-clone"); //Target the newly cloned and appended element
	}
	makeSticky(cloneExists);
});