I think the best way to improve a colony is to give them a boost by adding frames of brood from another colony.
You may not have another colony to do this with, so what I would do to add a package is first remove the old queen in the morning. Then about seven pm add the sheet of newspaper with slits cut in it, add the new brood box and shake the new package into the upper brood box. Being close to evening they won't want to take off and start flying right away and will settle with the queen in the open box. As soon as they have setteled into the box add a pollen pattie and your miller feeder, syrup, and cover.
Wait at least five days before opening it up to check for eggs. If you don't feel comfortable direct releasing the queen, then open after three days and make sure that they have released her.
It's also possible that if you have more bees in the package than in your old hive, that after ten or twelve hours of being queenless that you could just dump them in together. BUT I would not release the queen right away. In this case I would not even uncork the queen cage for a couple of days. After that you would only make a small hole in the candy so as to take another three days for the bees to release her. Error on the side of caution, you don't want your old bees killing the new queen.
