Does the contract have to be awarded between 5:00PM and 11:59PM on the same day as the announcement? Can the contract be awarded the next day? Can the contract be awarded before the announcement is made? Can the contract be released in SPS before 5:00PM, then awarded (furnished to the contractor - see FAR 15.504) after 5:00PM same/next day? Is there a better way to meet the CHINFO requirements without working outside of normal business hours between 5:00PM and 11:59PM?
The rules on announcement of contract award are found in FAR 5.303 and the DFAR/Service Supplements. I have included these supplements at https://acc.dau.mil/CommunityBrowser.aspx?id=680735 so you can see what is written. As required by the DFARS 205.303, notification to Congress (using the Public Affairs address) is made a day before contract award. Take a look at the various supplements and some require the notifications to go up through their internal communication channels up to 3 days before award. It appears consistent that all are making award after Congress has been given the information so that Congressman can be the first to make the announcement to their constituents of the award. (That is the purpose of this delay).
I see no reason why the Navy is forcing the award to be the same day as the public announcement. Your regulations do not require it. It's hard to be certain what individual offices are doing, unless an actual audit was done, but the regulations support the decision to award the contract the day after the public affairs office has been notified.