Mesa is hit and miss, it works for some games but not for others and plenty of artefacts at times. The Vulkan or DX12 backends are fairly fast, but not a perfect solution either way.
You can put opengl dll in the Teknoparrot folder and it should work. It was fixed a while back. Which dll do you put in which folder?
I will try to see if there is a way to dynamically load different versions of atioglxx.dll without changing the system files. I am busy this week but will check next week maybe since I have the same issue and did not think previous atioglxx.dll would work better. AMD drivers are garbage, that is why now I only buy Nvidia. But my portable device is AMD, so I have noticed some of the issues you mentioned.