If it's the same as the old set up, it will turn left from FHR into Therapia Road, right into Scutari, right into Marmora and right again to the bus stand by the Old Cemetary. Then start it's route from the stop opposite Therapia.
Of all the options I do like Drxysters best but that said, I don't think 3 months is that bad. The works will include the upper part of FHR at the juction with Brenchley Gardens so perhaps that is why there is a reluctance to divert up the hill.
It used to be permanent until the mid 80's. The old Routemasters used to use that route to turn before the traffic lights were put in on the FHR/Woodvale junction. How long is it expected to last for?