The SPA's we create can be reliably linked to (the current URL changes as the user moves around, even though the page hasn't reloaded) and they are "stable" because our business would go bankrupt if Google couldn't crawl our content.

If Google can crawl it, then you can too. And while Google doesn't use a headless browser (or at least I assume they don't) they absolutely do execute javascript before loading the content of the page. And they execute the click event handlers on every link/button and when we use "history.pushState()" to change the URL Google considers that a new page.

You're just going to get a loading spinner with no content if you do a dumb crawl (I disagree with that and think we should be running a headless browser server side to execute javascript and generate the initial page content for all our pages... but so far management hasn't prioritised that change... instead they just keep telling us to make our client side javascript run faster... imagine if there was no javascript to execute at all? At least none before first contentfull paint)