We investigate the formation of a laser-produced magnetized jet under conditions of a varying mass ejection rate and a varying divergence of the ejected plasma flow. This is done by irradiating a solid target placed in a 20 T magnetic field with, first, a collinear precursor laser pulse (10^{12} W/cm^{2}) and, then, a main pulse (10^{13} W/cm^{2}) arriving 9-19 ns later. Varying the time delay between the two pulses is found to control the divergence of the expanding plasma, which is shown to increase the strength of and heating in the conical shock that is responsible for jet collimation. These results show that plasma collimation due to shocks against a strong magnetic field can lead to stable, astrophysically relevant jets that are sustained over time scales 100 times the laser pulse duration (i.e., >70 ns), even in the case of strong variability at the source.