That's just not possible, and for good reason: some things happen now, and some things happen later, and if you need ultra-fine-grained control over what happens when, then you need to be very explicit about what's happening and how and when.
Green threads. No silver bullet, but sometimes you upgrade your pistol.
JS needs greenthreads. There's no reason you shouldn't just spin up a thread for every blocking context. This is arguably what async/await already does, but you don't have control over the toplevel loop. Point out where your while (userIsOnWebsite) { ... } loop is. :)
Having a toplevel loop is very important for simplicity -- but even moreso for what you mention: having ultra fine-grained control, and not constantly fighting with the underlying scheduler / ecosystem.