I can't see their difficulty. You tell the organisers you're planning to withdraw from the tournament, they tell what will happen if you do, then you decide what your next move is. If the price is too high, you let it be known you cannot guarantee it will be first team players turning up, due to pre-season plans etc. Otherwise you regrettably walk away and take the hit.
Otherwise this is going to fester until the damage is too deep to ever be repaired. The board appears to think the reputational damage of breaking a contract is worse than losing the goodwill of the support. It's a viewpoint they'll regret taking. I've spent a considerable amount of money these last few years that I wouldn't have spent if I hadn't felt it was helping get the club to where I wanted it to be. Without faith in the board, that support all goes out the window.