Sounds like it's my bare-bones basic soundcard that's limiting me.
I'm going to agree. In all the descriptions of people using RealTek sound cards (the built-in ones on laptops and some store desktops), I don't recall ever reading that anyone was happy. I hope someone here can prove me wrong.
In the meantime, you can certainly solve your problem without any jack contrivances if you buy a simple USB soundcard. Something like the Focusrite Scarlett 2i2 or 2i4 would do, and there are several competitors with similar equipment. Then you use ASIO with the DAW and the new soundcard, and MME or WAS with BIAB.