Don't know why they dont go the whole hog and do what we do in my bowling club for all our competitions and just draw every team out in order and play the ties down round by round by progression. Works at Wimbeldon and other major sports too. At least then you can chart your progress with anticipation rather than wondering how they'll keep the uglies apart until the final😉
Monday night at potentially 22.30/23.00 is hardly prime time tele though and a far smaller audience at a QOTS/Hibs tie than there will be for a Rangers tie.
It looks like the double draw is being made before the game at Ibrox (around 2pm) and I'm not sure it's on TV at all.
I'd have thought they were obliged to broadcast it to avoid any accusations of jiggery-pokery... All seems a bit of a mess.