Common internet Homebrew Rules I Don't Use

[Bareheaded Warrior]

I wouldn't consider either of those games complex, but I know what you mean. I make some simple changes to some monsters based on the logic of the game. Fimirs clearly have a battleaxe so they get 4 attack dice, Chaos Warriors have plate armour and a helmet so they gain a defence die, and skeletons have a long two handed weapon so they can attack diagonally. These all increas the monsters effectiveness slightly, which I think they need. I also upgrade my Gargoyle with an extra att die defence die and BP.

"Fimirs clearly have a battleaxe so they get 4 attack dice" - agreed

Fimir
MV = 6, AD = 4, DD = 3, BP = 2, MP = 3

"Chaos Warriors have plate armour and a helmet so they gain a defence die" - agreed but I also consider the variants

Chaos Warrior
MV = 7, AD = 4, DD = 5, BP = 3, MP = 3

Chaos Warrior (Stone)
MV = 5, AD = 4, DD = 6, BP = 3, MP = 0

Chaos Warrior (Doomguard)
MV = 8, AD = 5, DD = 5, BP = 3, MP = 4

Note: And I treat Festral's Personal Guard from ATOH as standard Doomguard

"Skeletons have a long two handed weapon so they can attack diagonally" - agreed (and I also equip Goblins with Spears to give them a diagonal attack)

"I also upgrade my Gargoyle with an extra att die defence die and BP" - agreed

Gargoyle
MV = 6, AD = 5, DD = 6, BP = 4, MP = 4

[Kurgan]

That's a good point, but modifying the monsters to reflect what the miniature shows is very Warhammery, and will certainly increase the challenge.

One way to simply (and often dramatically) increase the challenge is to let monsters defend the same way heroes do (count white shields instead of black as defense against skulls).

On another side note I appreciate that those extra toggles for monsters were added recently to the HeroQuest Companion App. Not that we couldn't simulate that before but it makes it even easier, just for those types of players who complain that the game is "too easy/boring" (probably overkill to use those things in the EQP/BQP though!).

[Bareheaded Warrior]

It isn't really about modifying monster stats to reflect what the figure is armed with, although it may appear like that.

In basic SE the Orc has Mv8,A3,D2,B1,M2 and the Fimir- has Mv6,A3,D3,B1,M3. The Fimir extra DD gives it a very slight bonus in combat over the Orc but its 2-point less movement rate effectively cancels that out (people often overlook Movement as important for combat, but higher Movement value generally increases your chances of getting the first strike in and for many monsters that might be their only strike!) so the Orc and the Fimir have very little distinction between them in terms of their stats which is poor when you consider that they are 2 of core 7 basic monsters and amongst the most frequently encountered.

So the decision to boost Fimir to have an extra attack dice is motivated by trying to keep a distinction between the two monster types, it just happens that it also aligns with the weapon that the figure appears to be carrying.

Same for Skeletons and Goblins getting diagonal attacks, it helps balance door blocking and allows these weak monsters to gang up and present a threat in numbers (diagonal attacks allow you to attack with up to 8 monsters at once, rather than just 4), again it just happens that for Skeletons this coincides with the weapon that the figure is carrying.

The Chaos Warrior / Stone Chaos Warrior / Doomguard / Gargoyle rebalancing is about keeping levels between the three "ranks" of Chaos Warrior -> Doomguard -> Gargoyle and also keeping stone monsters consistent Stone Chaos Warrior, Gargoyle and various statues and similar in other Quests. Although on this group an alternative way of handling this may be surfacing via the "Polishing the SE" thread so I may revisit these changes but the principles behind them are sound, stone things should be consistent, and elite Doomguard should be better than basic Chaos Warriors and so on.

[Kurgan]

[Edit: I should amend this because technically, literally, both 1st-1989 and 2nd Edition-1990 of HeroQuest did INDEED limit supply of Equipment based on cards. This was revised with the 1991 "Adventure Design Kit" box which provided a larger re-designed Character Sheet and instructed players to write items down on the sheet and that cards would not limit the available stock. Whether many EU players chose to adopt this official revision is unclear. But supply for Armory or Alchemist Shop items was never limited in the NA edition and explicitly is not limited in the remake edition which adopted the Equipment deck mechanic alongside the Armory concept].

(updated the OP with this correction)