I figured out how to do this. I'm actually doing this to help someone else. He likes to listen to music in a random order until he finds a song/artist that appeals to his current mood. He then finishes listening to the rest of the album. He has used Shuffle/UnShuffle in Winamp for years.
Since JRiver uses a dynamic Playing Now instead of a static list, it makes it a little more challenging since there really isn't an "original order" to Playing Now. Songs, albums, and playlists can all be added during the listening session so you really can't Unshuffle.
I don't think he cares if the playlist is in the original order, he just wanted the rest of the album to be in order. I found that all files are assigned a Filekey. From my brief checking, it seems that all files in an album are sequentially numbered in track order using the Filekey.
In Playing Now I added an expression column showing Filekey().
During playback of any playlist in random order, I can now click the Filekey column to resort and songs are now organized by album. I right click the zone and select Update Order. The rest of the album will now play in sequence before going to another album. After the album finishes playing, I can click Ctrl +R to reshuffle again.
I request a hotkey to resort by Filekey and update order so this can be done in Theater View.

It is kind of like the opposite of Shuffle, but really isn't an UnShuffle.
Why doesn't Update Order have a hotkey already? Is there any way to update order in Theater View?