So I just had some time to try out the USB Ethernet device again. This time I tried using MiamiDX instead, but with the exact same result. I managed to configure it using usbasixeth.device and was able to do a few pings but it doesn't take long until it crashes the USB stack and I see nak timeouts on the Ethernet in Trident.
So I'm thinking either a bug in the asixeth.class, usbasixeth.device, Poseidon or the RapidRoad driver. Since this adapter can work on an X-Surf clockport, perhaps it is some hardware/timing difference which triggers the error. Too bad it seems that this software is not being maintained so it can be fixed.