How can I elegantly increase the difficulty of Elder Sign?
One that is simple to implement, doesn't add any time, and seems to up the difficulty without making it overpowering is to ignore the word "unless" and everything after it on mythos cards.

So, for example, "Add a Doom token to the Doom track unless at least 1 investigator has a Spell." would become "Add a Doom token to the Doom track."

Particularly if you're playing with 4 players, these cards never seem to add doom tokens by the base rules. Another alternative would be to change "unless at least 1 investigator" to "unless ALL investigators".

That same thread has some simple rules for making the final battle harder, but I haven't tried that one. Definitely seems in line with your goal of being simple and not adding time to the game, though.