thank you all for your contributions. I changed to cycle renders and soon after that  I realized that moving viewport camera away from model removed the offset..  (???)

Now it's about all clean except in one place where a narrow path leads to a big cave.  Also I have noticed that when I use the texture paint across seam (using a dark texture over a white background) sometimes it leaves out white spots near the seams and I have  to paint it from a specific angle to remove the spots.

Strangely enough I exported model to poser and I had white seams in preview window everywhere I changed settings and the seams tended to disappear when moving towards the polygons. I have restarted Poser and the seams have totally disappeared...

thanks for your suggestions.  In the future I will try using smart UV as you pointed out. it seems a very effective way to use texture painting. any idea if it's also useful when baking normal maps?