That's really odd. I have heard/seen this happen in a few games along the years and its usually an problem that relates to specific game engine combined with specific drivers.
I have never heard of this type of issue being this persistent. 2 years and a GPU swap and still you have problems
Can you give a few examples of games where you have this problem along with the current driver version you are using. I'm assuming you are running everything at stock speeds. Your card is plugged in to the top most PCI-E slot right (the blue one)?
You might give downloading RadeonPro and adjusting the flip queue a try though I would not get your hopes up.
I have never heard of this type of issue being this persistent. 2 years and a GPU swap and still you have problems

Can you give a few examples of games where you have this problem along with the current driver version you are using. I'm assuming you are running everything at stock speeds. Your card is plugged in to the top most PCI-E slot right (the blue one)?
You might give downloading RadeonPro and adjusting the flip queue a try though I would not get your hopes up.