Grasses that have been developed for pastoral farming still lead to more methane burps. Current research seems to be focused on breading grasses / other pasture crops, and breading animals that produce less methane, Vaccines that could be given to animals, Inhibitors that could be added to their diet[1], and modeling of the methane formation process. But yes, the simplest way to reduce it would be to reduce the number of animals, by eating less meat.

[1] https://www.pggrc.co.nz/files/1501479614891.pdf