“even the Levush would agree that spelling words while playing Scrabble does not violate Shabbos since the letters are complete to begin with.”
That is what I have been taught.
“This precludes using a game where letters or numbers snap firmly into place, and prohibits playing Travel Scrabble on Shabbos.”
I have also been told to use regular Scrabble and not Travel Scrabble on Shabat.
We also have a simple way of keeping score: Bookmarks! Find a book with at least 300 pages. If you score 20 points, put the bookmark at page 20. If you score 13 points on the next turn, put the bookmark at page 33. It completely avoids writing. You need as many books as you have players. In fact, because we mostly play Scrabble on Shabat and rarely if ever during the week, this is our normal method of keeping score! Therefore there is no issur.