I am just going to say this...

We have tried perennial ryegrass in hayfields years ago.  For various reasons - which I won't go into here - it never really caught on.  However, I would think Glyphosate would do a good job of killing it.  It is hard for me to imagine that you are having an ongoing issue with Perennial ryegrass. If you truly are, it says to me that you are not getting it killed when you are trying to kill it.

Here, we have issues with Italian (or Annual) Ryegrass, and with Roughstalk Bluegrass.  Both of these are annuals. Both germinate in the fall, and head out in the spring. They are a problem in small grain fields like winter wheat.  Both are not a problem in summer months, and then new seedlings germinate again in the fall.  I am wondering if you are dealing with either one of these - instead of perennial ryegrass. 

So, my first thought is to suggest that you make sure you are dealing with perennial ryegrass, and not Italian or Annual Ryegrass.  .....