What are the next steps? Is there any way to get freshly manufactured fans for Z800?
Yes, the Z800 is a very noisy machine. I have one and fighted with this for a long time. When the Z820 came out i noticed that it was much quiter than the Z800 so i replaced all my fans in my Z800 with replacement fans for the Z820. It got better but it is still a noisy machine. If you decide to change fans, go for the replacement fans for the Z840 since they are even quiter.
Are any of the newer Z series workstations significantly more quiet? Will a modern Z440 be as fast or faster than a 7 year old Z800 with a single CPU?
My Z800 is: 2 x Xeon X5670, 48GB RAM.
When i retired the Z800 i bought a Z440 (G1X59EA) with 1 x Xeon E5-1650v3 and it is faster than my old Z800. I edit video and swithced when Adobe After Effects still had the multicore option and that was the only app were the Z800 was faster than the Z440. I was shocked when i turned on the Z440 for the first time, since it is dead quiet. It is still dead quiet after 1.5 years of daily use. If you buy a Z440 today, make sure to get one with the new Xeon´s, such as the E5-1650v4 instead of E5-1650v3.
I wanted to buy a Z840 but did not do it since i did not want to risk sitting with a noisy computer for five more years. (Five years was enough...)
The downside with the Z440 compare to the Z8X0 is fewer SATA ports and fewer PCI-e slots. For me it was not an issue but can be good to know depending on how you configure tha machine.