Make the prize for Sokoban a guaranteed amulet of reflection, and guarantee a bag of holding to generate elsewhere. It could be in any of:

• On Mines’ End, not replacing the luckstone but along it.
• Somewhere below Minetown, not necessarily at Mines’ End.
• In a vault in the Dungeons of Doom, not in the first few levels.
• Somewhere at or above the depth of Mines’ End, which could be in any branch.

However, guaranteeing the existence of a reward item like the amulet of reflection risks funneling players into a single standard strategy.

The Rat King Mines’ End level should be changed so that obtaining the luckstone doesn’t rely on getting into a sealed chamber by teleportation; it’s a challenge that is either completely trivialized if you happen to have teleport control or requires you to tediously step on a teleportation trap many times until you happen to be teleported into the sealed chamber.

A new Mines’ End variant that contains a guaranteed scroll of earth, gold golems, and an earth elemental as a reference to some Swiss folklore involving gnomes. Possibly also add a healer statue named Paracelsus, who was one of the first to name gnomes as such.

Make the Gnomish Sewers Mines’ End in EvilHack less aggravating for the player who lacks teleport control: instead of having to jump into teleport traps and teleport around the level randomly until winding up in the hidden luckstone room, make one specific teleport trap always direct to that room.

Mines’ End variant that is an actual mine, with many twisty corridors dug out of the rock, and many unmined gems in the rock. The luckstone is unmined, in one of several possible spaces, not adjacent to any corridors but not too far away from them, and certainly not as far away as in the Wine Cellar. A pickaxe will be guaranteed somewhere on this level.

If Orcish Town is generated, there should be a guaranteed “peaceful” Mines’ End where all the inhabitants, surviving shopkeepers, watchmen and the priest have fled. Chatting to the priest will make him ask you to clear the orcs out of Orcish Town, upon which chatting to him again will make him grant you a protection boon and give you a luckstone.

• Internally, this can be done by setting a global flag if and only if Orcish Town generates, and only load the peaceful Mines’ End if that flag has been set. If you manage to get to the bottom of the Mines without yet generating Minetown, you are guaranteed not to generate the peaceful Mines’ End, and Orcish Town will not generate either.