SIRIUS
I would guess that the spiralling motion of Sirius is just it orbiting the barycenter of its solar system, and, being very very close to our sun.
Look at the angular diameter, how big it appears.
In arc seconds, Mars is at least 3.5 arc seconds (am I reading that right?)
and, the motion of Sirius as it is supposed to orbit its "invisible companion" is just 6 arc seconds in two directions, 12 in total.
not entirely sure how to read the X axis on this one, but it looks like it moves 6 arc seconds from 0, 12 in total.
Sirius to me appears bigger than Mars on that image above.
The barycenter of our solar system is around 1 sun diameter
guess that means the radius of the suns orbit around the barycenter
so the orbit has a diameter of 2 suns maybe
if Sirius has a similar barycenter, and is close
it could move 12 arc seconds in total back and forth over the orbital period it takes around its barycenter
that should be 50 years
and, the largest of the gas giants, the one most often attributed to "sirius B", should have a similar orbital period
what people have missed, is that Sirius is close, very very close
that's the parameter they did not account for