Ultimately, you can't really bring mundanes all the way up to the outer limits of casters, not without seriously stretching verisimilitude. You can do it partway, but remember also, mundanes come in martial and skill varieties. Unless you completely fuse the two archetypes, you have a problem here:
-Mundane
--Martial. Supposedly good when it comes to putting down enemies
--Skilled. Supposedly good when it comes to resolving non-combat situations
-Caster. Good at enemies, and incidentally can solve more situations than skill can.
So as discussed previously, you have the non-mutually exclusive ways of dealing with it:
Role exclusivity - More a game-side logic. As is, the game has little of it, casters can do anything skilled or martials can, but the reverse is not true.
Mechanical equality - Everyone resolves the conflict using the same set of base mechanics. This necessarily involves expanding status effects and utility effects such that mundanes can make use of them.
Power at a price - This WAS the model used in prior editions, until the limiters were removed. The caster can do things more effectively or differently from the other characters, but he takes a real cost to do so.
So I suggest a combination application:
-First, open up skilled characters capabilities, especially towards the upper end of the scale. They need to be able to expand the scope of challenges they can resolve using skills.
-Second, open up martial characters combat options. Status effects, battlefield alterations, means of targeting alternative defense can be provided.
-Third, Partially fuse 'skilled' and 'martial', a 1:2 ratio each side wouldn't go amiss, making them more well rounded
-Fourth, open up magic, give everyone access to minor magic. Common stat buffs, wards and healing charms, such are a staple in the mythic aspect of the division. The rationale is simple, everyone can do martial things to some extent, skill likewise, but magic is somehow exclusive. Martial or skill actions draw magic from the world itself. What else were the simple acts of hanging up a horseshoe(wasn't for luck, it was to ward off the faeries), throwing of salt(it banishes evil influences or reveals them), or even the brief prayers offered up to the gods?
-Fifth, split magic. You have the things that work on the same basic mechanics as the warriors and skilled types, these remain on combat speed and limitations as Low Magic. You have the things that ignore the basic mechanics, these become High Magic.
--Low Magic then would be largely weaker energy bolts, brief buffs and short term control effects, which you can fit into the schematic as the controller specification. Its relatively weak and intentionally so.
--High Magic have greater costs in personal sacrifice and time. Battle high magic would then be dealing in greatly increased casting time, vulnerability and fatigue. Non-combat high magic requires ritual, foci and offerings.
-Sixth, If everyone is equipment dependent, equalize it. Require focus items for spellcasting power, much like everyone else needs their tools to be at full effectiveness. At the same time make the others less tied to their gear, build bonuses into class chassis.
-Seventh, limit magical knowledge. It doesn't matter what magic can do. It matters what one character can do with magic. The arrays of spells available are ludicrous, no magi of myth actually know anywhere near as many spells as a 10th level wizard.
-Eighth, Theme. While you limit spell availability, the fact remains that you require a certain degree of flexibility. So you take the restrictions as fields of magical knowledge, and expand capabilities within them(ala psi augments). Generalist wizards are not a low level concept.