Ditto, Martin
I just rebuilt an A712 about a month ago due to a leaky lower trans seal. If you're going to go that far you may as well replace dampers, motor glides, polish the pulleys, new belts, clean the transmission, new seals, etc... as a transmission service requires almost a complete tear down of the machine. You're so close to a complete tear down at that point you may as well just keep going.
New oil won't fix the problem unfortunately. If you're worried about it, add more time to the cycle? Or set it on spin with an empty tub to move the oil around? Or do as Martin suggests and use a space heater?