Nvidia Quadro 4000 2GB 256bit PCI-E 16x 2.0 Video Card - works ok with Premiere Pro

Here's the problem with the K2000:

It is based on the first-gen Kepler architecture, using a GK107 chip that made its debut with the GeForce GT 640 - and in fact is a slower-clocked version of the GeForce GTX 650. As such, the newest Nvidia drivers for that GPU now no longer support CUDA for such an older part, as Nvidia itself had completely discontinued support for all GPUs with Compute Capability 3.0 beginning with the release of CUDA 11.0. That means that the newest drivers will install, but CUDA will be disabled. That may force newer versions of Premiere Pro to the software-only rendering mode (no GPU acceleration whatsoever).

The K1200 isn't much better: It is based on the first-gen Maxwell architecture using the GM107 chip, whose Compute Capability version is 5.0. Nvidia, beginning with the release of CUDA 10.2, had depreciated all GPUs with Compute Capability below 5.2 (in other words, anything older than the second-gen Maxwell GM2xx parts). As such, CUDA capability for the K1200 will be locked to CUDA 10.2 compatibility even when running CUDA 11.x drivers.

And even without factoring any of the above points, the K2000 is clearly inferior (specs-wise) to the K1200. Higher numbered parts are not better, in this case. The K2000 has only 384 CUDA cores and a memory throughput of only 64 GB/s, versus 512 CUDA cores and an 80 GB/s memory throughput of the K1200.