Thanks so much for recording your playthrough, videos like this are so valuable to understanding the flaws in the game.
The random numbers aren't really random at all - they appear in a looping sequence. It's possible to 'use up' random numbers so that they get out of the way of the numbers you want. In the Randomlabs building there's a box which uses up a random number to pull an item from the pile - but I've noticed a few people miss it when looking around. This is because the box is never specifically mentioned, and the sprite makes it appear like it's a background decoration.
In version 2 I'll look into making the mechanics tighter and more refined, and make it easier on the player for understanding the sequence of events.
Thanks so much for your feedback!