With what little input I can say, is that CS6 has less effects supporting GPU acceleration. As Premiere CC evolved, more effects were written to support 'Accelerated Effects'.
So, have you tried adding an effect from Premiere CS6 effect panel, that has 'accelerated effect' and seeing if your Tesla is able to enguage?
There are posts from years prior that had users fighting your same issues. I cannot recall the final outcome, but believe there is advice from the past.
For CS6 the surest way to burn your money is to try the Maximus route.
For less than 10% of the cost of Maximus, you can use a faster better performing GTX solution.
The only situation where a Maximus solution may, just may make a tiny bit of sense is on a quad socket E7 15-core system with 512 GB memory running Windows Server 2012 R2, which is not supported by Adobe.
Your tip is very specific in tech sense , I am keeping it in mind .
Let us forget about money burning , think about long term investment .
See I always intent to burn machine let's say to do 20 channel composite output for 2K video , and sooner or later 40 for 4K .
In that sense MAXIMUS could be a wise choice , seeing that I have run a PCMARK's low end module of testing graphics pixel variation and then TESLA K40 did run at its summit level .
I did try a lot of things just as you said , but those would not do on dinosaur CS6 .
And lucky me there 2 tech men from NVIDIA and ADOBE have taught me how to awake GPU acceleration manually .
But lucky you you don't need to suffer those procedures .
so you have the Quadro and the Tesla paired in their nVidia GPU utilization graph - the Quadro shows activity, but the Tesla is flat line zero
and back in Premiere the Tesla is also recognized either by adding name to text file or deleting file - or just Premiere acknowledges the Tesla as you have set.
that’s how I see your problem, and if so, I'd like to see one of those set-ups flash a wave of colors around
I've been thinking about the Camera Raw plug-in in Premiere CS6 and twisting the Tesla into that, but the current updates to that plug-in come in from an account with Adobe's Creative Cloud