The design and optimization of laser-Compton x-ray systems based on compact distributed charge accelerator structures can enable micron-scale imaging of disease and the concomitant production of beams of Very High Energy Electrons (VHEEs) capable of producing FLASH-relevant dose rates. The physics of laser-Compton x-ray scattering ensures that the scattered x-rays follow exactly the trajectory of the incident electrons, thus providing a route to image-guided, VHEE FLASH radiotherapy. The keys to a compact architecture capable of producing both laser-Compton x-rays and VHEEs are the use of X-band RF accelerator structures which have been demonstrated to operate with over 100 MeV/m acceleration gradients. The operation of these structures in a distributed charge mode in which each radiofrequency (RF) cycle of the drive RF pulse is filled with a low-charge, high-brightness electron bunch is enabled by the illumination of a high-brightness photogun with a train of UV laser pulses synchronized to the frequency of the underlying accelerator system. The UV pulse trains are created by a patented pulse synthesis approach which utilizes the RF clock of the accelerator to phase and amplitude modulate a narrow band continuous wave (CW) seed laser. In this way it is possible to produce up to 10 μA of average beam current from the accelerator. Such high current from a compact accelerator enables production of sufficient x-rays via laser-Compton scattering for clinical imaging and does so from a machine of "clinical" footprint. At the same time, the production of 1000 or greater individual micro-bunches per RF pulse enables > 10 nC of charge to be produced in a macrobunch of < 100 ns. The design, construction, and test of the 100-MeV class prototype system in Irvine, CA is also presented.