We develop flexible and nonparametric estimators of the average treatment effect (ATE) transported to a new population that offer potential efficiency gains by incorporating only a sufficient subset of effect modifiers that are differentially distributed between the source and target populations into the transport step. We develop both a one-step estimator when this sufficient subset of effect modifiers is known and a collaborative one-step estimator when it is unknown. We discuss when we would expect our estimators to be more efficient than those that assume all covariates may be relevant effect modifiers and the exceptions when we would expect worse efficiency. We use simulation to compare finite sample performance across our proposed estimators and existing estimators of the transported ATE, including in the presence of practical violations of the positivity assumption. Lastly, we apply our proposed estimators to a large-scale housing trial.