This can be solved in two ways. First, like you said, refresh frequently. Alternatively, you can just click the "global" or "notes" tab on the page, or, like I do, fuck around on the forum while the game is processing. The other option is to not press ready when finished with your moves. It should be noted, though, that while this guarantees a full five minute phase, it also guarantees that at least half the board will hate you for taking the full five minutes. This should only be used if, for example, you need to go to the bathroom or take your dog outside and need to know when the game will process.