If the chipset does not work according to standards, then its broken. For some issues you might be able to workaround on the other side, but certain things can't be fixed.
One example which I know very well is the broken TI XIO2200A Firewire 400 chip. The main issue with this was, if I remember right, that it didn't reliably issue a hardware interrupt once data arrives. This you can't workaround on driver level.
From what I read in this forum basically the USB3 chipsets from ASMedia were bad.
For USB3.1 chipsets not 100% sure .. maybe there is not much experience with this, because you would normally save the "precious" USB3.1 ports (precious in terms of Bandwidth) for other things ...
I personally made the experience that my UFX+ worked well on a Startech USB3.1 PCIe card with ASM2142 chip in USB3 compat mode. No long term test but worked with my stress test project with 400 tracks.
But there is no guarantee that your newer Startech USB3.1 controller with newer chipset works the same ...
I think there are reasons if RME documents in the handbook that there are issues with ASMEDIA. I would for this reason recommend, to take this information as serious and simply take the stuff which is documented to work.
So either use the USB3 ports from chipset or do the same as me and get an additional card with the supported FL1100 chips.
The Sonnet USB3-PRO-4PM-E is a really fantastic card. It has behind each of the 4 ports a dedicated USB3 controller based on the supported FL1100 chip.
The driver for Win7 is really good as it uses the more efficient MSI driver model (message signalled interrupts). In Win10 drivers are provided automatically by Microsoft.
Although my Chipset on the board is an Intel C610, which normally works very well I came finally in trouble when connecting besides 2 UFX+, 1 ADI-2 Pro also additional peripheral stuff like USB3 bridge and USB Bluetooth adapter.
The only solution which really helped was to isolate the 3 Recording Interfaces / ADDA converter behind this Sonnet USB3 controller.
Now everything works like a charm and even with 2 UFX+ and ADI-2 Pro permanently connected via USB.
USB has some builtin "magic" .. somehow the devices seem to impact each other .. I don't know for whatever reason. But if the USB from Chipset is not stable enough anymore, I can only simply give you the advice to do what I did.
BR Ramses - UFX III, 12Mic, XTC, ADI-2 Pro FS R BE, RayDAT, X10SRi-F, E5-1680v4, Win10Pro22H2, Cub13