Now that would solve these problems and also grant greater immersion, so I'm totally behind this. Although it does add another layer of potential balancing nightmare. Hmm... making Quest XP universal spending points would work, but if the bulk of the experience gain comes from finishing quests that would defeat the whole purpose of splitting it up in the first place. So, maybe divide the XP you get from quests between Combat XP and Non-Combat XP percentually depending on how you solved the respective quest?
What if it was truly seperated into 3 different XPs (Bars/Levels etc.)?
So, instead of using Quest XP for distributing Combat XP and Non-Combat XP, it would be it's own thing.
Example:
Combat XP would be gained from combat, when you level it up you could then choose to increase something (via a perk or feat type system) from a list of Combat-Only abilities.
Non-Combat XP would be gained from non-combat tasks, when you level it up you could then choose to increase something (via a perk or feat type system) from a list of Non-Combat-Only abilities.
Quest XP would be gained from completing quests, when you level it up you could then choose to increase something (via a perk or feat type system) from a list of abilities that would be helpful in Quest-Related activities (traveling around the world via world map, teleportation, etc.), or even Party-Based abilities (since traveling around the world map is party-based).
The main problem I see here, is that there might not be enough perks/feats to place in the Quest category, but I could very well be wrong about that, as this idea is very new to me.