Symmetry breaking and yoga magic
You say that people perform magic by drawing on emotional memories, except for the hero, who does it some other way.
One solution would be, as you say, to bolt two different systems together. You can do that, but if that is what happens then your question should be closed because you'd be asking us to invent the entire second system for you, with the only acceptance criteria being that it not be driven by emotional memories; that would be far too open-ended for this site.
The only acceptable alternative I can see would be to grow a larger super-system around your memory system, and then explain how the additional parts grant the hero magic. (This is, in a weird way, an analog of the anthropic principle.) That is what I propose to do.
I take as my (loose) model the electroweak force and symmetry breaking:
In particle physics, the... electroweak force is the unified description of two of the four known fundamental interactions of nature: electromagnetism (electromagnetic interaction) and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 246 GeV they would merge into a single force.
Along those lines, we should consider the following questions:
- What is the larger mechanism, of which emotional magic is just one aspect?
- How and why did the larger mechanism give rise to two distinct aspects?
- What is the other aspect that grants access to magic?
- Why does the hero have access to the other type of magic, when it seems like nobody else does?
Emotions and memory are both completely private mental things. The obvious opposites would be public, physiological things. A "whole person" is a combination of their private mental states and their public physiological state.
If people can do magic by using one half of their whole self, it stands to reason that the ability has its origin in that unified self. And we're going to stipulate that the other half also provides access to magic, somehow.
We might ask: is there a time in a person's life when those two halves are not separated? I propose the answer is childhood, before the person becomes self-conscious enough to make a habit of distinguishing between their mental states and their physical states, a simple time when they just exist and the everyday experience of life washes over them as an undifferentiated stream of stimuli.
The picture now becomes clearer: something unusual happened in your hero's youth that led them to have more affinity for their public physiological state than for their mental and emotional state, and this affinity became entrenched when their human development reached the stage where they started to resolve that undifferentiated stream into its parts. The way this person experiences life, the seat of their identity is not the mind inside their skull, but rather their visceral and tactile body.
So, how does the public, physiological identity grant access to magic? It's a very common trope for spellcasting to require a physical dimension, usually hand or body movements, and that's how it is for your hero. The best fuel for their magic is not vivid and emotional memories, but exaggerated or even strenuous physical motion. Imagine something like an aircraft marshaller:
Presumably, the reason your hero has a lot of this kind of magic is that they are very fit and in touch with their body. Perhaps they are a yoga instructor, or a serious gymnast, etc.