Two major challenges in time-of-flight positron emission tomography (TOF-PET) are low spatial resolution and high radioactive dose to the patient, both of which result from limitations in detection technology rather than fundamental physics. A new type of TOF-PET detector employing low-atomic number (low-Z) scintillation media and large-area, high-resolution photodetectors to record Compton scattering locations in the detector has been proposed as a promising alternative, but the minimum technical requirements for such a system have not yet been established. Here we present a simulation study evaluating the potential of a proposed low-Z detection medium, linear alkylbenzene (LAB) doped with a switchable molecular recorder, for next-generation TOF-PET detection. We developed a custom Monte Carlo simulation of full-body TOF-PET using the TOPAS Geant4 software package. By quantifying contributions and tradeoffs for energy, spatial, and timing resolution of the detector, we show that at reasonable combination of specifications, our likelihood-based identification of pairs of first interaction locations in the simulated detector identifies 87.1% of pairs with zero or negligible error, and correctly rejects 90% of all in-patient scatters. The same specifications give TOF-PET sensitivity of ~66.7% and PSF width 4.6 mm with clear contrast. A detector with these specifications provides a clear image of a brain phantom simulated at less than 1% of a standard radiotracer dose.