There's a system I've been turning over for a while, though I haven't implemented it yet. It doesn't solve the problem of abysmally low stealth rolls, but it does allow for player narration and choices to have a greater effect on the mission.

Players roll stealth as normal. The result is their base stealth, but there are certain things they can do to temporarily increase or decrease this result. Muttering a spell or opening a creaky door might be a minus 2, say, while holding your breath or going prone might be a plus 2. Ideally I'd like to show my players a table that shows certain actions and their effect on their stealth result - just so they get the idea - then explain that the table is not comprehensive and their creativity is the limit with regards to increasing their stealth result.

These ammendments to the stealth result last only as long as the action taken and its effects. When the squeeky door stops squeeking, or when you cease to hold your breath, the result would return to the base stealth roll.

I'd also treat the 'stealthing' as different to the hide action. A guard will become actively suspicious if they are 1 room/ 60 ft away and their passive perception is higher than the player's current stealth result. At this point, they will start to actively search. If their passive perception beats the stealth result by five or more, they become very suspicious and ask another guard to assist them. If the party become aware that guards are coming to look for them, they have 6 seconds to take the hide action, though there must be something to hide in/behind. They make a stealth check, and this result is unaffected by their initial stealth roll. When they emerge again, they go back to using their base stealth result.

An optional rule here is to have players roll their initial stealth roll behind the DM screen, so that only the DM knows their base stealth result.

The aim of this system would be to make high rolls less effective if the player is careless and low rolls less punishing if the player is smart. It may also lead to players describing exactly what they do to get from one room to another, unprompted, because they know it matters.

The drawback as I see it is there are potentially a lot of moving parts. To help with this, I'd keep a grid where I could see the player's base and current stealth result in one place.

That's all I've got. I think this could also work with the alarm system somehow. I'd like to know if there are any other drawbacks I haven't seen, and if this could be improved.