Hi,
> - native open source drivers
> - supports at least three monitors
> - PCIe x16
> - support for 4K
> - HDMI output
> - audio not necessary
AMD cards are going to be your only options here, because the two choices
for open source drivers are AMD and Intel, and Intel doesn't make
stand-alone cards with multi-monitor support. (With some laptop models, you
can drive the internal display plus one with the built-in external HDMI plus
one over thunderbolt, for a total of three displays, but that doesn't sound
like what you're looking for.)
I personally have been very happy with AMD cards (previously, a Vega 56 and
now a Radeon Pro W5700) on Fedora Workstation -- they basically just work,
and provide a great gaming experience.
Those are in a completely different range from what I was thinking.
$800 for a video card? And only using the open source driver?
My comment about using an open source driver was based on the need for
stability, but if the binary driver provides better support for the
card, and is still stable, then I would consider that as well.