Yeah, indeed quite extreme. The 3rd object would have to have an extremely short orbital period I would guess, < 1 d?
If the 3rd body's orbit is not coplanar with the system orbit, then that would quickly destabilize, right?
If the 3rd body's orbit is coplanar with the system orbit, then it should transit both stars, negating any sufficiently large eccentricity in the third body's orbit, which one would think might be fatal in such a cramped space.
Transits of the host star would be at regular intervals. Transits of the other star are guaranteed regardless of the third body's orbital parameters, but they would occur sporadically without a resonant effect which might be nice for system stability.
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