Anyways, my questions are (a) has anyone else had stability problems with connecting Thunderbolt displays via their onboard ports/iGPU, and (b) would this add-in-card potentially help?
If the problem is with the iGPU then not using the iGPU would help. I don't know how well mixing iGPU and Nvidia works. I avoid it because iGPU support seems broken in Hackintosh for multiple displays.
If I use it purely for mini-DP video output, not even connecting my motherboard's headers, it should function as basically an expensive active video adapter, right?
The GC-ALPINE RIDGE doesn't have mini-DP output. You need a USB-C DisplayPort alt mode to mini-DP cable for that. The GC-ALPINE RIDGE has the following functions (I don't think any of these functions require the header cable because they all seem to work in macOS on my Z170X-Gaming 7 which doesn't have a Thunderbolt add-in card header):
1) Two 4 lane DisplayPort 1.2 to USB-C DisplayPort alt mode adapters.
2) Two 4 lane DisplayPort 1.2 to Thunderbolt 3 adapters.
3) Dual 4 lane DisplayPort 1.2 to Thunderbolt 3 adapter.
4) Two port USB 3.1 gen 2 controller with 2 lane DisplayPort 1.2 alt mode capability for each port.
5) Thunderbolt 3 NHI (not useable on hackintosh yet?)
6) (I'm ignoring the HDMI output of the GC-ALPINE RIDGE because I don't know what it's good for since it's only HDMI 1.4)
It's the only solution that does all that so I don't think you can call it expensive. The Sunix UPD2018 and Delock 89582 don't have Thunderbolt and only have one DisplayPort input.
But if I do connect my mobo Thunderbolt headers to it, would performance be any different than the existing onboard Thunderbolt? Thanks.
Your onboard Thunderbolt controller only gives you one Thunderbolt 3 port and it has only one DisplayPort input so you can't do 5K or two 4K displays, and the input is from the iGPU. The second Thunderbolt 3 port is USB 3.1 gen 2 only with no DisplayPort.
The GC-ALPINE RIDGE has two DisplayPort inputs so you can do 5K or two 4K displays and you can choose to use the IGPU or your graphics card, and it has two Thunderbolt 3 ports. Other than that, there's no performance difference.
The Thunderbolt NVM firmware versions may be different. For example, The GC-ALPINE RIDGE has a newer version than my motherboard. It doesn't look like Gigabyte will ever upgrade my Z170X-Gaming 7 Thunderbolt NVM version. I don't know what version your motherboard has. It doesn't look like there's a firmware update for it yet. Intel should not have given control of the firmware updaters to the motherboard manufacturers because they won't update them.
https://communities.intel.com/thread/111547