With regard to the separation of Beta Muscae being a puzzle, I have the WDS data file for this pair, which I obtained some time ago.
Early measures were erratic, to put it politely; including repeats by some of the same people. Back around 1900, the separation was most likely around 1.2" to 1.3" and changing pretty slowly. It became wider, and by the late 1940s was about 1.40" (Simonow at Stromlo; van den Bos in Johannesburg).
It didn't widen much more after that, and by 1991 Hipparcos got 1.206" with the same year a speckle measure by Hartkopf (4-m scope) giving 1.201". No doubt the third decimal is cancy with these.
By 2015 Tokovinin with 4.1m and speckle got 1.0218"; Rainer Anton using "lucky imaging" (0.5m scope) had measures of 1.010" and 1.002" in 2016: say 1.005"
So, the mentioned 0.8" is not something that's happened in the last 100+ years. 1.4" fits for mid-20th century; and for more recent dates you have the numbers above.
Beta Mus had an orbit calculation done in 1964, and it was a pretty bad effort. The Orbit Catalogue gave it a Grade 5 rating, which means it's not regarded as being much more than a first attempt.
More recently (2012) there's a new orbit, the period now is given as 194 years, near enough half the period of the older orbit, which had a 383 year orbit. The new calculation, although looking more plausible (helped by another 50 years of measures) is also Grade 5. It will help when Beta Mus has travelled more of its orbit.