I know the cheapest fare you can get in advance to ORD from MIA is $231. Even if the lowest advertised fare is $178.
Also for peak periods and holidays, get your flights 3 months in advance as guess where people want to go for their holidays??? You guessed it. Miami (unless they prefer the thrill of potato farming in Idaho.)
The 777 is on the 6:35 a.m. out of MIA and the 6 p.m. out of ORD. The others are 737's.