I've posted this before, but I think the way to increase difficulty is:
1.) Leave damage around the same as Normal, but ensure enemies are able to cause the same amount of damage to you. Armor could be made more effective at stopping certain types of damage over others.
2.) Make it more difficult to heal. Stimpacks could work much more slowly, or have a cooldown. Crippled limbs would require a doctor or special doctor's bag to heal (more like the original Fallout).
3.) Radiation, starvation, poisoning should have more meaningful long-term effects. It starts off as an inconvenience but can become a major problem over time if not dealt with.
4.) More deadly environments. I'm NOT a fan of being one-shotted in any circumstance, but things like traps, radiation pockets, and monkey puppets just aren't scary enough. Failing to notice a tripwire at full health should leave you alive, but in a world of hurt.
5.) Food and nutrition should be necessary, but I really wouldn't want to be interrupted every 5 minutes to manually enter the Pip-Boy and scroll through inventory to eat and drink. Attaching a sort of "auto" feature would be nice. You must keep food and water in your inventory, but you don't need to micromanage it. I think attaching this to the "Rest / Wait" function would be the way to go.
6.) More ways to avoid combat altogether. It would be lovely for the game to provide characters ways of circumventing, negotiating, bribing, or distracting enemies and still being able to complete quest objectives. And faction actions! The flare gun for the Minutemen is nice, but why could I not arrange for other factions to send people to a location in advance. You arrive, and signal the attack. You can't control them like companions, but they can still back you up.