I think with full time study 4 months is eminently possible. One issue is that you need to book the 2 wk residential brushups in advance, usually 1-2 months, sitting the exams straight afterwards. This would mean booking the brushup and exams for Mod 1 as soon as the coursework arrives. BGS usually want to see a certain amount of progress and results before they'll accept a booking for the brushup, and sign off an exam application. This is not a show stopper, but will require close liaison with Alex Whittingham, as it is him you'll need to convince that you are competent and will be ready.