A pair of experiments is presented for measuring intra-methyl 1H-1H dipolar cross-correlated spin relaxation rates in highly deuterated, methyl protonated proteins with significantly improved sensitivity relative to previously developed experiments that measure dynamics via 1H spin relaxation. In applications to proteins with correlation times in the macromolecular limit, these cross-correlation rates are related directly to order parameters, characterizing the amplitude of motion of methyl-containing side-chains. The experimental approach is validated by comparing extracted order parameters with those obtained via 2H and 13C spin relaxation methods for both protein L (7.5 kDa) and malate synthase G (82 kDa), with excellent correlations obtained. The methodology is applied to study Ile, Leu, and Val side-chain dynamics in a 360 kDa "half-proteasome" complex. In particular, order parameters obtained from the WT complex and from a second complex where the proteasome gating residues are deleted establish that the relative levels of dynamics in each of the two molecules are very similar. It thus becomes clear that there is no communication between gating residues and other regions of the molecule involving pico- to nanosecond time-scale dynamics of these methyl-containing side-chains.