This paper focuses on the problem of optimal bit and power allocation in linear periodically time varying (LPTV) channels in broadband (BB) power line communication (PLC). Previous work has demonstrated that improvements in bit loading can be achieved with LPTV channel adaptation via so-called microslots in time for an orthogonal frequency division multiplexing (OFDM) system. In this paper, we present that the application of a power constraint that is averaged over many microslots can be exploited for further performance improvements through loading. Due to the matroid structure of the optimization problem, greedy-type algorithms are proven to be optimal for the new LPTV-aware bit and power loading. Significant gains are attained especially at reduced transmit-power levels, where the energy per bit-transmission is also low, and for poor (i.e. high attenuation) channel conditions. Furthermore, two mechanisms are utilized to reduce the complexity of the optimal LPTV-aware bit loading and peak microslot power levels: (i) employing representative values from microslot transfer functions, and (ii) power clipping. Our results indicate that the reduced complexity LPTV-aware bit loading with power clipping performs very close to the optimal LPTV-aware bit loading, which makes it an attractive option in a practical setting.