Sounds like you want to keep a healthy chunk of power-upping at each level, but want to eliminate binary effects from impeding story-telling. First level and twentieth aren't that different in that regard:
1st: "Whoops, greataxe." This is when hit points don't count for much, and saving throw modifiers are so puny as to make the saving throw mechanic irrelevant. Anyone being hit in the face with a greataxe at level one is probably going to be out of the combat.
20th: "Whoops, Baleful Polymorph/Confuse/Wail of the Banshee." Hit points, while not irrelevant, are so huge at this point that saving throw effects are more useful and game-affecting.
Similarly, with higher levels come other binary effects. Along with "Oh, you're dead" come "Oh, we're there" and "Oh, she's alive again."
Hit points, traveling, and quests to resurrect party members all have something in common - they extend the story in a way that has continuity, for lack of a better word. There's something in between 40 hit points and -10; there's something in between the Keep on the Borderlands and the Mines of Chaos, there's something in between the Paladin falling in battle and his body being carried in the back of a cart pulled by galloping horses to the temple of Pelor while the army of orcs batter down the gates to the city.
But there's nothing between alive and Slay Living, there's nothing between being in Verbobonc and suddenly being in the Inner Fane of Tharizdun, and there's nothing between being dead and then being slapped on the shoulder by the Pope of St. Cuthbert, who coincidentally happens to be your adventuring companion, and whose Asmodeus-concussing just got interrupted by your inconvenient death. ("Dude, you took time away from my buffing!")
During the "sweet spot," hit points are relevant and the loss of them is scary and suspenseful, making saving throws is suspenseful, travelling is a story, and death is something to be feared, but isn't completely insurmountable.
Don't make it take longer to level, just try to make hit points more relevant, saves more relevant, travel more relevant, and death more relevant. Consider nerfing spells such as Confuse (make the chance of acting normally a higher percentage) and Slay Living (maybe it hacks off 50% of the target's HP this round, and the other 50% the next, with a cool-looking purple lightning bolt connecting the caster's hand and the target), assign quests to resurrections ("Bring Us Hextor's Umbrella Rack," intones the Solar assistant to Heironeous, "We Shall Into It Insert An Amusing Device. Upon Completion, We Shall Bring Your Barbarian Back To The Realm Of The Living. Again."), or make it so that Wizards can only teleport once a day and are exhausted after doing so. Maybe Flesh to Stone takes five rounds to finish, with a more debilitating effect each round, and is stopped by the death of the caster.
And I wouldn't make it so that you only get new hit points at fifth level, but new spells at sixth, IMO. That may work for others, but I'd feel cheated as a player myself.
