Objective. Prompt gamma-ray timing is an emerging technology in the field of particle therapy treatment verification. This system measures the arrival times of gamma rays produced in the patient body and uses the cyclotron radio frequency signal as time reference for the beam micro-bunches. Its translation into clinical practice is currently hindered by observed instabilities in the phase relation between the cyclotron radio frequency and the measured arrival time of prompt gamma rays. To counteract this, two proton bunch monitors are presented, integrated into the prompt gamma-ray timing workflow and evaluated. Approach. The two monitors are (a) a diamond detector placed at the beam energy degrader, and (b) a cyclotron monitor signal measuring the phase difference between dee current and voltage. First, the two proton bunch monitors as well as their mutual correlation were characterized. Then, a prompt gamma-ray timing measurement was performed aiming to quantify the present magnitude of the phase instabilities and to evaluate the ability of the proton bunch monitors to correct for these instabilities. Main results. It was found that the two new monitors showed a very high correlation for intermediate proton energies after the first second of irradiation, and that they were able to reduce fluctuations in the detected phase of prompt gamma rays. Furthermore, the amplitude of the phase instabilities had intrinsically decreased from about 700 ps to below 100 ps due to cyclotron upgrades. Significance. The uncertainty of the prompt gamma-ray timing method for proton treatment verification was reduced. For routine clinical application, challenges remain in accounting for detector load effects, temperature drifts and throughput limitations.