No let up in aggression... I don't think this is going to work.
Ink,
I wish there were some others that have done this that would chime in.
Until then, looks like it's just you and me here. First, don't get discouraged just yet, it's only been a day!

. Take a deep breath, walk away from the tank, and let the angels settle in. The egg-crate is ugly, but it isn't going to kill anyone.
Are either fish showing any signs of distress? If the Regals are feeding, then there is nothing to worry about. You waited a year for your new fish, what's another few days or even a week or two?
Also, don't compare my "apparent" success with what you are doing; The circumstances are not the same. I had the luxury of a separate, dimly lit tank that I keep the fish in alone, and the significant difference in size may have made the process a little easier. Also, don't be fooled into believing that I have "paired" my diacanthus's. They just happen to be getting along right now in the tank.....whether or not they actually pair will have a lot to do with their care and nature (not to mention the fact that I'm not absolutely sure the smaller fish is even a male!)
Something you may want to do before you give the fish a little 'space' is to re-arrange the rock-work. Again, this is not fun, but in light of everything you have waited for and the prospect of having these beautiful fish happy together, it's not a big deal. This may help to "reset" their "territory", and could possibly lead to less aggression when you remove the egg-crate for round 2.
I have read in two separate threads from people who have successfully paired Regals.
1. One of the people recommended keeping the fish separated in the same tank for over a month, before introduction. (Think this may have been Copps, who has several Regals together)
2. The other had to try four times with the same two fish before they would get along. The 1st time he said the new fish got beaten so badly he thought it was going to die. The 2nd and 3rd times there was still a great deal of aggression. The 4th time he put them together, they got along like magic....with no evident explanation of why.
Chin up, and be patient. Keep me (us?) posted.