I don't mean separate ASIO software installation, I mean there were options when installing Uni drivers, one was for an ASIO installation. How that differs I'm not sure. Whether it just installs ASIO as well as the drivers, rather than having to install ASIO separately, or whether the drivers work differently in some way, I don't know.
The idea though, is that ASIO allows software to directly take control of the device, which removes other processing by Windows, which may be the cause of the added delay. Whether that would solve the problem though, I don't know.
For some reason using a USB headset must be free of this extra processing which is adding to the delay. Really a USB headset should be no different to a sound card. The microphone and headphone parts of any headset are both analogue, so both have to be converted to and from digital, which has to add some delay, even if it's not perceivable. That's either done within the headset in the case of USB, as it's a digital connection, or the sound card does it if the headset just has analogue jacks.
There might be a solution, but I'm stumped as to what it is, other than buying an audio interface which is designed for this kind of thing.