Cavemen should have a mugh higher natural Strength cap, perhaps all the way up to 25.

New artifact The Golden Knight, a gold small shield that has the following properties:

• Sets strength to 25 when worn like gauntlets of power.
• Cannot be invoked directly, but if you fall below 25% of your HP maximum when your invoke timeout is good, it automatically invokes itself to take half of your current Pw points and heal you for that much HP.

If this doesn’t seem powerful enough, remove its strength effect and make the base item a shield of reflection instead.

When monks are weak from hunger, they don’t lose any Strength, due to being experienced with fasting.

You can use #force to pry open doors with edged weapons; however, this requires more Str and has a higher chance of breaking the weapon (perhaps dependent on the weapon’s weight.)

Wielding a one-handed weapon with nothing in the offhand will double the damage bonus from Strength (but not weapon damage or other bonuses).

Walking up stairs exercises Strength.

The quest-text associated with the Sceptre of Might suggests it confers strength. So the +n Sceptre of Might acts like a +n ring of gain strength.

Condensing all of NetHack’s poison mechanics into one unified mechanic:

• Dexterity and Constitution poisons are removed. Quasits (the only AD_DRDX attack) might still directly harm Dex, but it’s no longer flavored as poison. Rabid rats (the only AD_DRCO attack) don’t cause poison, they cause disease, which hits Constitution. Poison will now only affect Strength.
• Poison is now implemented as a timing-out trinsic. The amount of Str loss is a direct function of how much timeout is left, so Str will gradually recover as the poison goes away.
• Passing Con saving throws could give small bonuses to decreasing the timeout faster than normal.
• While poisoned, HP regeneration is either impeded or stopped entirely, or else the player’s HP is damaged every turn, or every several turns.
• It could also heavily abuse Str while it lasted instead of being directly tied to Str.

Strength should not give a to-hit bonus; the encumbrance system is already there to address that.