Christian Buil has just posted some high (R ~ 38,000) resolution spectra which confirm the reduction and narrowing of the H alpha line seen in my medium resolution spectra. He also detects a small (4.5km/s) shift in the line.
http://www.spectro-aras.com/forum/viewtopic.php?f=38&t=2433&p=13796#p13792
These observations may be consistent with the partial obscuration of the star as suggested from the VLT images. The speed of rotation of the star is of the right order as can be seen in this reference and the axis of rotation is given there
https://www.obspm.fr/the-slow-rotation-of-the-red.html?lang=eng
As far as I can see, the orientation of the VLT image is not given though unfortunately.
Jeremy, are you still in contact with Prof. Constantino Sigismondi? I wonder if these observations might be of interest
Cheers
Robin