LAPET is a LaBr3-based whole-body time-of-flight PET scanner. We previously reported coincidence timing resolution 315-330 ps (fwhm) in benchtop measurements and 375 ps in full-system measurements. We are currently testing prototype units for a complete redesign of LAPET's electronics, aimed at further improving full-system timing performance and at preserving that performance at high count rates. We report on four facets of the new design. First, PMT-by-PMT high-voltage control at two points per dynode chain permits both gains and timing offsets to be equalized across the scanner. Second, analog pulse shaping reduces the duration of each PMT pulse from 75 ns to 35 ns, reducing pile-up effects. Third, custom circuit boards use the DRS4 waveform-sampling ASIC to provide oscilloscope-quality readout of each PMT signal, enabling digital processing of PMT waveforms. Finally, an FPGA-based trigger provides the coarse energy and timing measurements used to detect coincident pairs. Tests are underway of prototype High Voltage Control boards, Shaper/Analog Mezzanine cards, and the DRS4-based Module Readout Board; the Master Coincidence Unit design is in progress.