In Summation by Parts Operators for Finite Difference Approximations of Second-Derivatives with Variable Coefficients (2012) by K. Mattsson, SBP operators for second derivatives with variable coefficients have been introduced. These could be used here to use narrow-stencil SBP operators for the semidiscretization for the BBM-BBM equations with variable bathymetry. In SummationByPartsOperators.jl they are accessible by var_coef_derivative_operator and source Mattsson2012().
EDIT: SummationByPartsOperators.jl does not implement variable coefficient second-derivative SBP operators for periodic boundary conditions yet.
EDIT2: See ranocha/SummationByPartsOperators.jl#258