I know you changed the start menu after someone asked for it to be changed to view the compendium from the start menu, but I feel this damages the elegant one button click and load demon used to have. I was tempted to just ask for you to undo the change, but a solution that might satisfy both: have the old click save to begin system/game auto start if you have no saves... but also have an icon you click above or below to check the compendium.
The other thing I was going to suggest: For Cycle 2 and beyond, maybe make small changes to make it repetitive? Increase the chance of Modifier demons and rare encounters and possibly a smal chance of adding an extra demon to an encounter. This would both add additional variety and challenge to new runs