Ok your SSD appears to be a Samsung EVO 850 which is a SATA III device, it also appears to be connected via the spare SATA port in the optical drive bay. The SATA ports for the optical bay and the SATA ports for the four standard hard drive bays are all SATA II meaning they can only do 300MBps speed. SATA III could in theory do 600MBps.
I do not know the exact speed your Samsung drive is capable of but if it is similar to my own SATA III SSD it will be in the region of 500MBps. So firstly it is going to be limited due to your using SATA II to less than 300MBps since you never get 100% effective speed. In other words probably nearer 250MBps rather than 500MBps exactly as your own results found.
To give you a comparison of what would be possible, a Samsung AHCI PCIe type SSD drive connected via a PCIe adapter would be able to get close to 1500MBps! For the mathematically challenged that is six times as fast as yours.
If your interested in one of these faster SSD drives see the following.
https://www.amazon.com/Lycom-DT-120-PCIe-Adapter-Support/dp/B00MYCQP38/
https://www.amazon.com/Samsung-512GB-Express-Solid-state/dp/B0179DQM34/
And a speed test comparison - http://barefeats.com/hard200.html
As I am sure you already expect a traditional hard drive is much slower than an SSD. In fact even though some hard drives do come as SATA III compatible drives they cannot get anywhere near the speed of SATA II let alone the speed of SATA III.
So it does seem your storage speed is very likely to be a significant contributor to your problem. I will repeat my advise to run the BlackMagic Disk speed test as it specifically rates the results against the requirements for editing various video resolutions so you will instantly see if it is good enough for 4K requirements.
Note: It is possible via two different approaches to add SATA III interfaces to your Mac Pro so you can run your existing Samsung drive at its full speed, however as indicated above even if you do this you will still only get around 500MBps which will still be only a third of what the PCIe style SSD drives can do.