Naproxene syntheses: electrophilic aromatic substitution on activated naphthalene
No other byproducts are shown


I haven't checked the original Syntex patent (if you've ever written a patent you know that sometimes important details are omitted), but it seems odd to me that those two isomers are claimed to be the most significant isomers formed. As you point out, the 2-methoxy-5-acetoxy isomer is not expected to be formed in significant amounts based on electrophilic substitution patterns in substituted naphthalenes (Note: here is a nice concise reference that shows how to apply the same concepts used to predict which isomers will  predominate in electrophilic substitution with benzene to substituted naphthalenes). 

In this abstract the Friedel-Crafts acetylation of 2-methoxynaphthalene is studied.  By changing solvents they can shift the major product from 2-methoxy-3-acetoxy to 2-methoxy-6-acetoxynaphthalene.  These two isomers are among those expected and the experiment shows that these two isomers are close enough in energy that small factors can significantly impact the product distribution.  Two other factors to keep in mind


the 6-acetoxy isomer corresponds to "para" substitution
When running a Friedel-Crafts with oxygenated (hydroxyl, methoxy) aromatics, the aluminum chloride will (depending to some degree upon solvent) complex with the oxygen.  In the case at hand this could make the methoxy a bulky substituent disfavoring reaction at the ortho positions.



  But again, why in pos. 6? Why not in pos. 3, in ortho to the
  activating substituent?


Careful low temperature mono-bromination of phenol shows that para-substitution is strongly favored (>95%, reference).  If additional bromine is available a second bromine will be substituted at the ortho position. It seems that the same thing is happening here in your 2-naphthol example.

Like you, I might not have predicted these outcomes, but that's why we run experiments.


  are these reactions done under kinetic or thermodynamic control?


Sorry, without more information (like product composition as a function of time, temperature, etc) I can't answer that.