Ascending Armor Class at the time of 3rd edition was a major intuitive and time saving innovation. But what is more important is how it points to rolling over as a consistent concept. The OSR darling Lamentations of the Flame Princess runs with this when it makes Dexterity the target number to hit a character is not wearing armor. This rule and Ascending Armor Class really do open Pandora's box if you are willing to step further away from D&D traditions.
In the original game there were saving throws of various kinds like "Death Ray", "Dragon Breath", "Paralysis" and "Petrification." From OD&D to AD&D to BX and BECMI these seemed to morph. And in the greater OSR they continue to do so. Swords &Wizardry, Labyrinth Lord, Flame Princess, etc all seem to have their own take on saving throws. But there was also another kind of save - the stat check - where you took a d20 and tried to roll under your ability score. Remember when you had to roll under your Dexterity to make sure you don't slip on that log while you are crossing the river or some similar situation?
What we are going to do here is invert that mechanic to follow something more akin to an attack roll where the attribute is the target number. Rather than have the player make an awkward check it might seem better to have these environmental and situational elements attack the character instead. Simply choose the appropriate ability score as the target number and roll a d20.
So when you have an unarmored character, and attack him with a sword you try to roll over the character's dexterity score. The poison when ingested tries to roll over the king's constitution score. The giant constrictor snake tries to roll over Conan's strength score. Lying is an attack on intelligence. Roll against the Guard's wisdom of 8+(1d6-1) to see if your distraction worked. Have a crowd attack a character's charisma when the character is trying to rally them to fight against the invaders.
The possibilities are endless. This more adversarial approach may bring more drama and tension. The log is not steady and sound, its wet and slippery and it may betray you. This solves the grapple issues and more easily moves checks related to the environment behind the screen if needs be - I roll all rolls in the open but others may not. It may or may not replace the old school (and new school?) saves but your mileage may vary. But in the end the player is no longer rolling against themselves but rather the stats are being directly tested against things in the environment which seems to open up the game more.
*In an old computer hacking zine from the 90's there is a landmark article called "Smashing the Stack for Fun and Profit" this article borrows it's name from that article.