First, define your accuracy standards. Second what is your budget?
I do agree that a new build is the best course if budget allows. Might sell the Colt to cover part of it.
A few other thoughts. Consider 18 or 20” barrel. Consider just buying a trigger and building a good upper and adding a UBR STOCK.
Also for your needs consider a .204. It will shoot circles around a .223.
T he 77 grain .223 bullets are not a good choice for 300 yard coyote shooting. You want something that will shoot a fairly flat trajectory and open up. 55 grain .223 or 32 grain .204.
But, what do I know? I have not shot a coyote for almost 20 minutes and only killed 2500 or so in my life.