To shred or not to shred my rye

I'm in east Texas and we have had rain on top of rain. I have had no window to cut my 150 acre meadow. All rye grass has already started to brown and on top of that, the heavy rain has laid it down. I did not fertilize as I rarely do on first cutting. My debate is if I should shred the rye and then fertilize my coastal and bail that. Or should I go ahead and bail the rye even though it will be just a filler with no nutritional value. All insight is appreciated

To shred or not to shred my rye