If you have the same type of ball but just a different color you should be allowed to switch. The USGA does allow it.
Since this game doesn't, what I do is use the last of a ball on unlimited play CTTH rounds. If the ball runs out and I post a lousy CTTH score as a result it's no big deal to me. I can always play it again with a different ball.
Or, just use that last ball for a practice 9 hole round. That way it doesn't affect your average; you can just quit the practice round when the game reverts back to the cheap balls.