In numerical approaches to differential equations on a lattice, accurately reproducing continuum momentum behaviour up to the band limit requires non-local derivative operators. We present efficient linear-combination-of-unitaries (LCU) block-encodings for the first-order derivative and Laplacian in the N = 2n-dimensional SLAC representation. The dense LCU amplitudes are prepared using a procedure closely related to coherent rejection sampling, exploiting their smoothly decaying structure to achieve low gate complexity and high success probability. We further use Shannon wavelet transforms to construct multiscale representations and diagonal preconditioners that substantially reduce the condition number, while exploring their performance beyond standard elliptic operators. Finally, we benchmark the logical resource requirements of the SLAC block-encoding using Qualtran and discuss its potential application to quantum algorithms for differential equations.