Use an Osma bottle gulley inside the garage, and feed the waste and rainwater in via the back inlet. Set the gulley top flush with the finished floor level, and fit a sealed lid instead of the grid, this will allow rodding access to the branch if required. Fit another bottle gulley externally to take the garage rainwater, (if permitted), this allows both laterals to be rodded if required.
I assume the existing main run is accessible at either end from the current chambers?