We previously developed a fast, local, reduced scaling Cholesky-decomposed multireference averaged-coupled pair functional (CD-LMRACPF2) method, which takes advantage of the locality of dynamic correlation and numerical approximations such as Cholesky decomposition and integral screening. Motivated by the desire to study large biodiesel methyl ester molecules, here we validate CD-LMRACPF2 for the computation of bond dissociation energies (BDEs) in a suite of oxygenated molecules, and show that the low-cost method is very accurate compared to the conventional variant. We then demonstrate the power of CD-LMRACPF2 for fast and accurate computation of energies of molecules containing up to 13 second-row atoms within a polarized triple-zeta (cc-pVTZ) basis set. We use biodiesel methyl esters as a chemically interesting model system and furnish BDEs of C-10 and C-18 methyl esters, with the latter performed within a cc-pVDZ basis set. We describe trends in the BDEs and explain how structural (isomeric) differences affect BDEs, as well as discuss implications of BDE trends for biodiesel physical and chemical properties.