You are completely correct. Would just like to point out the LK demon flip actually is an OS.
You can do this sort of double OS with J.LK OS lk demon flip OS cr.mp. It really removes the “reaction” aspect you mentioned. If your lk hits, you don’t cross up (like you mentioned),your OS lk demon flip will not come out, and you hit (hopefully lol) with cr.mp which your can hit confirm into c.st.hp.
As for the OP, when your opponent doesn’t tech get-up, the safest, most basic thing to do is to walk back a bit and play your solid footsie game. So your mixup didnt work. you’re still at an advantage because your opponent is on the ground. Think of it as starting the round with you at a big advantage lol. Until you find a solid answer like the double OS above, I think this should be your starting point.
could always go for that shimmy > throw to start your mixups again. could also walk up and block. overhead on their wakeup works wonders. it’s all about training your opponent. Street fighter is about setting precedences.
Always keep pressure on your opponent, even if that pressure is walking up and blocking.