Further, you can reinforce the uniqueness of the supernatural, etc. occurring in each adventure by starting out with a description of the mundane events of the characters' past before the adventure
I'm not sure that actually works. In my experience, players tend to gloss over the stuff that they don't actually play. -SAYING- they have mundane adventures in between is all well and good, but it doesn't mean much to them when every adventure they do have includes those other elements. To the players, everything they do involves the supernatural. Like I said before -- that means that the supernatural ISN'T weird or unexpected anymore. If your players fully expect that the BBEG is a sorcerer or is controlled by one, or that the mysterious disappearances of citizens is caused by a supernatural being, then you've already lost the Hyborian feel, because players shouldn't be -expecting- that. And if every adventure includes it, they will expect it.
I can only speak from my own experience and my own group. I know for a fact, because we've talked about it, that if I included the supernatural in every adventure, they would elect a new GM. None of my regulars (all Howard fans, except for one) feel that using sorcerers or monsters in every adventure is appropriate to the setting. They want to be surprised when it happens. And no matter how much I -tell- them that life is generally mundane, if they don't experience things without the supernatural involved, everything I -tell- them will be meaningless.
One of my players came to my table from another where he had gotten his old group to play Conan. He described this problem to me very specifically. It had gotten to the point in his old group that whenever something bad happened, the party immediately starting looking for some clue as to who the sorcerer or demon was, because it was inevitable that in every adventure, there was one or the other lurking around somewhere. He made it clear that he didn't feel like it was Hyboria anymore, because the supernatural was too commonly occuring.
"well, your character finished his daily job at the blacksmith, so now he has a couple of drinks at the tavern, gets in a brawl, and sleeps exhausted through the night, only to wake up and do it again the next day." Yay. Might as well just go to your day job if you're just going to play mundane stuff.
That's ridiculous. So if you're not using monsters and sorcerers, your games are about being a blacksmith? Please. What about getting trapped deep in Pictland and having to cut a swath of death through their ranks to get back to civilization? Or what about maneuvering politically among the Merchant Houses to play them against each other? Or raiding merchant vessels off the Western coasts? Or getting embroiled in a tribal war in the Black Kingdoms?
One of the games I ran that my players still talk about was almost entirely mundane. The characters found themselves lost in a swamp just off from the border of Stygia, and got attacked by giant snakes and (regular-sized) leeches. Then they came across a group of men led by a Merchant-adventurer that were attempting to harvest lotus blossoms to sell. Players got attacked and left for dead, but followed the group (largely for retribution). Ended up making it to Argos where they fell afoul of the guard of Messentia after killing said Merchant-adventurer. Spent some time on a stolen merchant vessel (they stole it, that is). Got attacked by Freebooters and washed up on the shores of the the Southern lands. Finally ended up in Kush where one of the players made himself a king, and was then killed by a rival Kushite. The other players (and that player's new character) killed a bunch of sacred shamans, fled Kush and ended up battling a sorcerer back in Stygia that, turns out, had been the reason they were disoriented and lost in the swamplands from way before.
That's a Conan adventure, and it went for about 25 sessions before the sorcerer showed up.
If you only find games exciting when sorcerers and monsters are around in force, there are plenty of settings for that - like Forgotten Realms and Dragonlance. The great thing about Hyboria is that there are so few beings of the supernatural (comparatively), that the world can just be visceral.
That's how I play it, at least - and that's how my group likes it.