Clover can be killed easy enough but keeping it that way is another story. I would have a professional come out and advise you before trying much of anything. You need to ID all the weeds you want to get rid of. Then decide on a budget, irrigation, seed type, mowing et. Good pasture grass can be a real value if established like yours is. Another thing is you make no mention of shade, fences, neighbors. Where is your house? In the middle? On one end? A common plan here is to have a real nice care intensive area for the home and the rest is just well mowed and sprayed once or twice a year. A large wonderful lawn is very time and money consuming. Think about some of those things. Make a trip to a lawncare store and get a few prices. Talk to your neighbors. Go to your nearest university extension. Do not just start pouring in time and money. You have time to find out and then act with a plan. That hay field might begin to look better after a look into things.