There already is one in ARIA that supports this: aria-owns [1] and to some degree aria-flowsto [2]
But with everything in ARIA, it always depends on real-world support of screen readers, which is very poor. You have to work with what actually works unfortunately.
Imo changing order just to change the streaming order for a tiny performance gain is not worth breaking the UX for people with accessibility needs.
tabindex only affects tab order (of interactive elements), not the order that a screen reader navigates and reads out content (including non-interactive elements)