In this paper (which is a follow up of the accompanying paper by W. Dröscher) an in depth analysis of three recent gravitomagnetic experiments is given. These experiments are unique, since there is a possibility that extreme gravitomagnetic fields outside general relativity might have been generated. The experiments were carried out in entirely different environments and are not related in any aspect, except that the effects reported are dependent on cryogenic temperatures. Furthermore, completely different measurement techniques were employed. The set of three experiments comprises the two laboratory experiments by Tajmar et al., Graham et al., and the NASA-Stanford University Gravity Probe-B space experiment. The physical phenomena observed could indicate the existence of novel physics outside both general relativity and the standard model of particle physics, and also would have major implications on the standard model of cosmology. Qualitative as well as quantitative comparisons between a physical model (Extended Heim Theory (EHT), which predicts the existence of extreme gravitomagnetic fields under cryogenic temperature conditions) and experimental results are presented. Several, so far unexplained, observations will be addressed. For instance, a physical explanation for the signal decay in the different experimental setups in the experiments by Tajmar et al. as well as the so called parity violation, seen in both experiments by Tajmar and Graham, will be given. Moreover, the difference in signal strengths between rings and disks, as reported by Tajmar etc., will be discussed. The tangential acceleration and deceleration of the four Nb coated quartz spheres and their mutual interactions in the GP-B experiment are explained through the existence of extreme gravitomagnetic fields. Finally, in order to clarify the currently non-conclusive experimental situation, a gravitational (Gedanken) Aharonov-Bohm experiment is portrayed that utilizes the interference of matter waves to measure the impact of such fields, being independent on the magnitude of gyroscope data, and, if feasible, would provide a yes-no decision on the existence of extreme gravitomagnetic fields.