Update to 5.3.6 introduced the "each page refresh" issue again (though PW didn`t seem so sluggish this time, yet it was a bit slower than usual), and
the fix worked again
Final result - updated to 5.3.6 successfully, and done playing... for now :P
edit: I rushed to call it working, it went back to each page refresh, and now even letting it fall asleep by itself does not help (it helped once, but as soon as I closed and reopened the cover it was back to each page refresh)... Tried with both 3.5.5 and 3.5.6. Could it be the heat in the end? We`ll see once it get a bit colder (as AC didn`t change much so far) :P Phew...