Thanks for playing my entry! Glad you enjoyed it.
Endless mode is enabled after you finish the game, which is any point after you reach the gun and the "My name is David Abbernel" line again. The line after "I got charged with murder" is simply something like "and I'm sorry", which just closes the game. The "AI" intentionally maxes out at this point so you will fail. You didn't miss out on much! If you've reached this point you should have unlocked the endless mode, which is automatically opened when you relaunch the game. The Endless mode should display a loading screen unless the words.txt file is small enough to be loaded near-instantly. (You can also substitute the contents of words.txt with your own dictionary if you wish, which can reduce load times.)
As for the difficulty scaling, it definitely is a hit-or-miss. If you check the source-code and understand GML, you can see that the difficulty scaling is literally just three variables-- the most important of which is used to determine how long the "AI" waits (in frames) to type the next letter. I really implemented the difficulty scaling with the intent of creating a difficulty curve as the story went, and then after that I worked to also make it so the intro sequence can effect what difficulty you start with using the system already in place. In hindsight, I should have probably thought to make the difficulty scaling first and then figure out the difficulty curving. I also could've put some more checkpoints along the way. It's something for me to keep in mind next time!
If you're interested, the here is the source code. And as you've already noticed, there is a full play-through on my YouTube channel as well.
Once again, thank you for playing my game and giving me your feedback!