Does the transport of oxaloacetate across the inner mitochondrial membrane during gluconeogenesis require carrier proteins other than those used in the malate–aspartate shuttle?

When authors of general biochemistry textbooks mention carrier proteins involved in the transport of oxaloacetate across the inner mitochondrial membrane for gluconeogenesis, they only make use of the two transporters involved in the malate–aspartate shuttle. As a result of only using the malate-2-oxoglutarate and the glutamate–aspartate carrier proteins, I show that the reaction describing the overall process is unsatisfactory since, in addition to oxaloacetate being transported from the mitochondrial matrix to the cytosol, 2-oxoglutarate is also transported in the reverse direction. I therefore point out that, if only oxaloacetate is to be transported from the mitochondrial matrix to the cytosol, then it is necessary to also make use of other carrier proteins in the inner mitochondrial membrane, namely, the dicarboxylate transporter and the phosphate transporter.