Battery (Li-SOCl) voltage varying with orientation
Ok, after some additional research I think found some useful information from other manufacturers. I will just quote some points of interest.

From Technical Brochure LTC Batteries


  Depending on mechanical cell design and system 
  properties, there is a certain dependence of available 
  capacity on cell orientation during discharge. The effect 
  is caused by the tendency of the electrolyte to move 
  towards the void and inactive space of the battery if the 
  orientation deviates from the preferred direction. The 
  capillary effect of the cathode and separator pores acts 
  against this tendency. As a result, the orientation effect 
  is smaller for thin cathodes than it is for thick ones and 
  is not even observable when discharge currents are very 
  low or when batteries are moved during discharge
  [...]
  At the high current end, available capacity of big cells 
  (C, D, DD) is affected if the batteries are discharged 
  upside down. Therefore this orientation should be avoided if possible.


From Handbook Primary Lithium Cylindrical Cells - VARTA


  Under upside down installation, the capacity of smaller
  size (1/2 AA, AA) is less affected whether discharge current is high, nominal or low. However, the capacity of bigger size (C, D) especially at higher discharge current is
  affected. Under upside down installation, the lithium and
  cathode is located in a fixed area whereas the electrolyte
  falls to the bottom in this case. At the top of the cell there
  is a space leaving an area of the anode and cathode, not
  covered by the electrolyte. Bigger size cells have a bigger empty space, so the capacity decrease in upside
  down installation is higher than in cells of smaller size.
  (About 20~40% of its capacity at same higher discharge
  current.)  


While we are not "at the high current end" and are using a AA cell, the measurements from above confirm that "upside down" is the worst orientation. 

So orientation does absolutely matter when using Lithium-Thionyl-Chloride cells. Learning never stops...