I agree, it seems that you have enough room for the length of the card.

For compute-only GPUs, you just plug them in any way you can if your power supply has enough wattage to support it. You can even get 16x to 1x pcie slot adapters for just that purpose. 16x vs 1x basically means slot length, in our context. (It's commonly done for Bitcoin mining.) Compute is different as it generally doesn't have the low latency requirements that a game would. PCIe is very robust when it comes to backward compatibility.

When it comes to running and AMD card and NVIDIA card together, I know windows handles it OK. I am not sure about Linux compatibility or what issues you may see.