An update on my situation:
Had a family member find a couple of other USB type-a to type-b wires at work. I tried the first one I saw and everything works as intended; so far with my ideal streaming software and the Roxio software open, the output hasn't switched from HDMI to component. Of course, as with most capture cards, there is a delay when the feed is shown through capture software (I guess it depends on the computer and such) but that's an easy fix by just giving a delay to my microphone and any other audio I have on a stream.