Largest smallest unattainable score in Scrabble

Consider the following Scrabble board:

We can play NO for 1 point, AI for 2 points, NOSE for 3 points etc as indicated on the right. All this obviously depends on having the correct letters on your rack (not shown). Eventually we will reach a number N such that it is impossible to score exactly N points on our next turn.

Let us say the "smallest unattainable score" of a game-state is the smallest positive number N such that we cannot score exactly N points on our next turn. The game-state includes both our rack and the board (we ignore the opponent’s rack for simplicity). Can you construct a game-state with the largest smallest unattainable score?

Assume that the CSW19 dictionary is being used.

EDIT: The game state must be reachable by valid plays (no phonies)

For partial credit: to simplify the problem assume that the board state contains only one word.

SOURCE: The Scrabble board was cut-n-pasted from Wikipedia.

Thanks to FlanMan for a recent Scrabble-related question