My apologies for taking so long to reply. Been a long and busy week.
I finally got to sit down and test these suggestions and neither disabling the in-game HUD or switching to window capture resolved the issue. I also tried both suggestions at the same time with the same results. The issue is worse when streaming over recording. It also does not occur when not streaming/recording, even with Broadcaster open.
I also wanted to make sure I tested with both AMD graphics driver versions 21.1.1 and 21.2.1 as I was on 21.1.1 at the time of original writing and the issue is still continuing under both driver versions. Current Broadcaster version is 4.0.2007.2911.
Not sure if this will be helpful or not, but I am using software (x264) encoding with these extra encoder parameters for streaming: &ex:threads=16&ex:rc-lookahead=60&ex:trellis=1&ex:aq-mode=1&ex:direct-pred=spatial
For recording I use the AMD HVCE.
Extra settings in the Radeon Software stack that I have enabled as well: Virtual Super Resolution, Radeon Anti-Lag, Radeon Enhanced Sync, Radeon Image Sharpening, FreeSync Premium. Though a few of these were accidentally turned off during my test of 21.2.1 driver as I forgot to go into the software to turn them on, but having those features turned off didn’t make any difference.