Intel is the only supported 10G PCIE cards. The newer and cheaper Aquantia cards are not supported out of the box.
My initial goal was to tinker with the NAS, and (try to) add the Aquatia Linux drivers to do some testing. I will hopefully still do that at some point, but .. not now. Unfortunately some work stuff popped up that will take me down a rabbit hole for a bit, so I probably won't have any time until October.
For now I've popped the Aquantia card into my workstation, and an Intel X550-T2 into the NAS. Though this particular Intel card isn't officially on the Synology HCL, it seems to work fine out of the box, as you say. So far it's impressive but timing is bad and the NAS is doing a RAID scrub, so I can't really see where performance is just yet.
I'll definitely want to look around a bit for tweaks, such as tinkering with jumbo frames. I'm not sure what flexibility I have on the NAS side, but will look into it.
Edit: Just wanted to make one thing clear that doesn't concern me, but might concern others. The X550-T2 is a 4 lane PCIE 3.0 card. The 1817+ has an 8 lane PCIE 2.0 slot. If you do the bandwidth math, there's enough for about 1.5 10G ports when using the card in this device. I'm only using 1 port, so the extra port and PCIE3.0 bits are just gravy for when the card gets re-purposed later on. Someday this will probably find its way into one of my PCs and I don't want it eating 8 PCIE lanes. Plus, I seriously doubt that I can saturate 1 10GbE link with my usage, let alone 2 of them at 75%.
Anyways, if this bothers you, there's a single port X550-T1 for about $50 less ($300).. and of course the 8 lane PCIE 2.0 X540-T2 using older silicon, with less features, and negligibly more power. They cost $500 new and legit, or as little as $100 to roll the dice on a knockoff gray market card. Hopefully choices will improve, and future Synology products will move to PCIE 3.0
I initially didn't notice that the current model is using the older standard because the NIC compatibility list contains a bunch of PCIE 3.0 parts. However, they are 8 lane cards so bandwidth is ok. Naturally a glance at the NAS specifications list reveals this plain as day.