I would give them a +1 to any ability score.
I would support a +1 to all ability checks - it simulates those higher stats but won't apply to attacks or damage.
I would give them an extra hit die for healing every day - humans go harder for longer.
This is pretty close to what I would like to see.
- + 1 to any one ability score
- + 1 to untrained ability checks/skill checks.
- Some sort of "grit" or "luck" mechanic - your extra hit die seems like a pretty decent idea.
- A culture-centric ability or a secondary background.
- A feat.
For demihumans, give them a + 2 bonus in their primary stat (or + 1 in primary and the secondary in subrace) so the implied setting is coherent and then;
Dwarves - They're actually quite good. However, Revise;
Dwarven Resilience: Change Immunity to Poison to Advantage to saving throws versus Poison.
Elves -
Elf Weapon Training: Add - Long Swords become Finesse Weapons.
Free Spirit: Give them an inherent + 1 bonus to Will Saves and change Immunity to advantage on saves versus Charm and Sleep effects.
Give them some manner of tactical mobility (specifically in woodland settings) - Brachiation (movement speed in trees or advantage on climb checks to move through trees) from 3e, woodland stride from 3e (the ability to not create tracks), or 4e's ability to ignore difficult terrain while shifting.
Halflings -
Give them something to emulate their natural charm, slipperiness, or guile within social interaction.