Don't know what your plans are for the field, but don't forget that rushes make great shelter -and shade- for sheep, especially lambs in a wet, windy Spring.
If you can use a flail topper it'll mash the stalks more than a blade, which'll help it get incorporated.
Whether the cuttings will choke the grass depends on how thick the rushes are, how windy the spot is, etc. If you can see grass through and between the rushes, and the rushes aren't thick up higher than your waist, it'll probably be fine.
Just realised you're topping 3-4' grass too.. Can you get some cattle on to graze it?