Currently the sensor performance of large ring laser gyroscopes is limited more by stability in the long term rather than measurement resolution. This is mostly because of a variable contribution of backscatter coupling between the two counterpropagating laser beams inside the square ring laser cavity. Introducing an atmospheric pressure stabilizing vessel around the ring laser structure allows us to compensate variations in the compression of the ring laser body by ambient pressure changes. Adding an interferometric feedback system takes this approach one step further in that it allows us to stabilize the length of the cavity to be stable to within 1 kHz of optical frequency. However it transpires that this precision cavity control is not sufficient to keep the backscatter coupling sufficiently constant to reduce the variation of the offset bias of the gyroscope to values of 10 µHz or below. A tightly controlled perimeter does not preclude small variations of the 4 individual sides of the gyroscope. In the absence of sufficient control over the backscatter process or sufficiently precise numerical estimate of the backscatter variation, a tight control of the length of the four individual arms of the gyroscope, in addition to the precision perimeter control appears to be a viable experimental approach. Monitoring the phase relationship between the ring laser beat note, taken at different corners of the gyroscope, provides the necessary access to the desired cavity control. This paper reports the first results of this investigation.