Hardcore mode, then, is where to test your mettle. In this mode, enemy lethality is cranked up to Brutal, ensuring that enemy AI are stronger, will prioritize squishier targets with low AC, and will seize opportunities to go in for the kill. Additionally, many adjustments have been made to the fights themselves specifically for Hardcore mode, with certain enemies receiving additional support through reinforcements, spells, or consumable items.
If you wish to increase difficulty Long Rests should require more camp supplies. 400 per long rests would give you enough supplies for 4-6 long rests during Early Access content which is plenty(I average about 4 Long Rests per complete play-through of EA)
Also increasing the bad-guys' initiative is another great way of increasing difficulty. When the bad-guys act first the good-guys take damage. This could be done either with a flat bonus to creature initiative or giving creatures the Alert feat.