Minor point but I think these are actually stone
doors rather than stone
doorways as all doorways in HQ would be stone.
More importantly, being doors, you would assume that all the standard door "handling" rules would apply unless otherwise stated, and the only stated difference in handling these doors in the quest book is that you need to roll to determine whether they open or not, then I think the official rules are clear: Opening doors is a free action that you can do as many times as you want on your turn as part of movement. You need to roll to determine whether the door opens or not.
However, whilst the official rule is clear, it is also flawed, failure in your attempt to open the door has no effect other than the door not opening, so you are free to try, try and try again. The outcome is inevitable, the door opening, the only thing that varies is the amount of player boredom.
In the spirit of keeping modifications to a minimum, keep it simple, less is more, and all that, I would suggest that failing the stone door opening roll should come with a penalty of at least ending your movement (but if you haven't used an action this turn you still can) or ending your turn (which feels a little harsh but then I'm not sure what action you would ever take in that situation so both options may amount to the same thing, and failing a roll ending your turn would at least be consistent with traps).
Nothing wrong with making it an action, but it is a bigger modification than is needed to fix the original flaw, less is more!
Also to keep this roll consistent with other such rolls/tests in HQ, allowing for the fact that there is very little consistency here anyway, I would suggest using the corresponding mechanism for the spell break test, so:
Player rolls a number of combat dice based on hero type, needs at least one
to open the door, failure ends their turn.
• Barbarian = 4
• Dwarf = 3
• Elf = 2
• Wizard = 1
This has the added advantage that the Wizard can now open these doors, eventually, which is better than him being the only hero not slain and then dying of thirst if he ever gets trapped behind a stone door, not a particularly heroic end...
As already suggested you could allow the Potion of Strength to boost your chances, roll an extra combat die or two, although despite the image showing your bulging muscles, the Potion effects actually boosts your attack strength, even if attacking with a Crossbow, but I still like the idea of the potion boosting your chances with the door.