Hi Bucks Mum
DS2 is tending to do the same - finish as quickly as possible, stop the timer and shout "done!". Last time he did this he finished with 7 minutes to spare. I gave him a ten minute break, then asked him to come back and use the 7 minutes to check his answers. He found a couple of errors, and then agreed with me that he should have used the extra time, rather than just stopping when he did.
If that doesn't help, I think I would back off at this stage - you risk him burning out. (Been there, got the scars!
When he is in a good mood, have a chat with him about it all. Say that you understand that he is fed up with all the practice and remind him that there is very little time to go now.
Then say that you also understand that checking his answers is a chore, but does he realise that he must do it in the real tests? You could ask him to tell you the rules that he knows he must follow in the real tests - circling questions he has guessed/not answered, using every minute of the time allowed, etc.
As long as he knows the rules and says that he will apply them in the real tests, I would just say to yourself that, from now on, the practice papers are just an opportunity to keep him sharp and keep the techniques at the top of his mind.
Hope that helps.