Putting it together - High Level Martial Examples
So taking what we have brainstormed, lets put out some examples of high level martial abilities that could take over some "magic only" areas while still maintaining some martial flavor. Note: These are just for examples, I'm not trying to make them super polished or come up with the best names or anything.
Perfect Lie - On occasion, you can tell a lie so convincingly, that it causes the target the question their own memories. If you get a natural 20 on a deception check, and the check was a success, you may adjust the targets memory as if using the Modify Memory spell. The modified memory must be relevant to the lie in question (determined by the DM). A person subject to this ability can not be affected by Perfect Lie again for 1 week.
Honestly, I wouldn't require a natural 20. 5e dropped many example of DC for skill use. A DC 30 check is "Nearly impossible". What is possible and impossible depend on what is peak ability for a skill use within the game world. Let's take Deception as you propose. It can, obviously, allow you to have your party enter a stronghold by passing something for a gift. Ulysses did this in Troy, and that was DC 20 to me (people actually thought it would work when the plan was described to them, so it wasn't extraordinary, just a very smart thing to THINK of it). How would you rule a character specializing in Deception who would try to do the same, bypassing most of the defences? What could higher DC checks do? What DC would you assign to convincing Martin Guerre's wife that you're her husband returning from war after a few years? What DC for starting a panick about a plot to kill a king, resulting in many people being convicted despite it being fake news, like Titus Oates did with the popish plot? Nearly impossible would be even more extraordinary Deception use than that. Convincing someone who was a direct witness of the truth, recently and with an interesting in remembering the scene correctly, that his memory is fuzzy, would be in the 25-30 range, and well within ability of even a mid-level liar. When a character is made prisonners by two guards, what is the DC for convincing one to kill the other in order to keep the (inexistant) bounty for the character's head for himself?
We lack example of high DC range as they will depend on how fantastic you want your world to be. But for example, a DC 30 Athletic check allow one to escape Dimensional Shackles, a rare magical item preventing evasion, including magical one. I'd allow Athletics, on the same basis, to let someone push through a Wall of Force. It's a "only" a DC 20 check to break chains and manacles after all.
What DC would you assign to Errol Flynn's "ladder of axes" scene where he climbs a wall using a few axes he threw just before? Sure, if you ask for 30, then your definition of mundane might not align with the definition of one who would assign 15 to this maneuver...
I think the "perfect lie" is the way to go, powerwise, if you want to change the balance of classes to something more to your liking, but the baseline of what skill checks can do is very fuzzy in the first place, with extreme variability (Athletics doesn't let you reach the actual world records, yet it allow a random commoner to break manacles 5% of the time, and I suppose real life people don't escape manacles daily when they are arrested (or we'd build better manacles...)
What is the DC of the religion check to pass as a cultist? That you're a priest of the cult? To pass as a priest in an oecuminical council? To start a schism splitting the religion into two hostile groups, leading to centuries of wars and massacres between them?