Be aware that it takes quite a good while before newly seeded grass has deep durable roots. It would be best if you could keep the chickens off it all year; at the very least, til late in the summer.
A heavy-traffic turf seed mix, with various fescues, would probably be your best bet (endophyte-containing fescues are not the very healthiest grazing for livestock but I am not aware of there being a particular problem with chickens and nothing else in the north is likely to hold up as well). Till the soil first to loosen it, and check the soil pH to see if you need to lime (a little while before reseeding, not at the same time)
That is still not *that* much run space if you want some of it to stay vegetated though -- how many chickens do you have? If it is more than just a couple, you may be out of luck in the long run. You might consider making one run (perhaps the new one) your "managed pasture", and only letting them out in it as much as the grass can gracefully tolerate, and use the other run as a "sacrifice paddock" that they are confined to when the grassy run needs to recuperate. Don't cheat on recuperation time either or you will gradually run the pasture into the ground again.
Good luck, have fun,
Pat