In which way would the yeast cell cope with the excess amount of methionine in the growth media?
In humans, cysteine first fills the glutathione pool (which itself is a reservoir for cysteine, apart from reduction equivalents and biotransformation). Excess cysteine can go three ways,


oxidation to sulfoalanine and further hypotaurine and taurine, via still unknown enzyme(s)
degradation to lanthionine and toxic H2S
degradation to serine and toxic H2S


Since cystathionine gamma lyase which (its L-cysteine desulfhydrase activity) catalyses 2 and 3 has homologues in yeast, my guess is that H2S is produced there too. Further oxidation of H2S happens through an ancient mitochondrial pathway which is highly conserved as well, yielding sulfite and sulfate. Sulfate then makes for a bit acidic environment but else is non-toxic.

I have linked to reactome.org entries where you can find references. Filling up the yeast's glutathione pool (if it happens) would move the NAD+/NADH balance to the NADH side, i.e., fill up reduction equivalents, too.