Can I split this hive?

Lost all 4 of my hives this past winter. Installed a new package on Memorial Day weekend. The Queen laid great, gave me lots of brood in June. She went missing in early July and then I saw Queen cups and the brood was diminishing. Checked a week later and queen cups hatched and gone - no queen to speak of, still a little brood left and I waited another week for a mated Queen to return. Checked last Wednesday - no Queen, no brood left. Purchased a new queen and 2 Nucs arriving tomorrow, checked hive today - no brood BUT A NEW QUEEN in hive.

Question: Since I have 2 deeps of bees and the new Queen has not begun to lay yet, can I split one of the deeps off tomorrow and introduce the purchased Queen and separate them as two separate hives? I've never done a split before and although it's late in Maryland, what if I added a frame of brood from each 5 frame Nucs to the newly separated Queenless deep, would that work? I have plenty of empty drawn comb for the new queens to get up to speed.
Any suggestions would be appreciated, thanks!