Indirect Area Control Mechanic

1)
The way you describe it, in abstract terms, it seems like a complicated mechanic, but it definitely is not. I haven't had a look at your complete rule set, but I wonder how the mechanic is actually implemented in the game. Are the area equations and influence equations themed? Or simply presented in the abstract. This could make a big difference to the accessibility of the mechanic.

For example, if the game were representing political territorial control, then the three aspects might be represented as cultural bias toward military might, economic development, and acquisition of knowledge. An example region A might have the 'equation' (+1, +3, -2), indicating a mild appreciation of military might, a profound admiration for economic achievement, and a disdain for scientific endeavour. An example of an action card might be a policy of pacifism, which may perhaps be (-2,+1,+1). In this case, i suspect it would be easier for folks to get the mechanic initially, and make it more intuitive to play in general. (I don't think this example will apply directly to your game, but what I'm trying to say in a roundabout way is that if you can use more concrete concepts then it should make the mechanic much more intuitive - since eg. anyone can realise militaristic people are going to be peeved with pacifist policies)

2) If players can only increase an attribute, and if a majority of the control equations on the board (ie. 4+ of 6) have a negative in one (same) aspect, then players cannot make intentional efforts on their part to exhert control over those regions with respect to that aspect (if I understand your description correctly - they cannot 'adapt'). The risk of this is that the event cards may become too significant in these games (ie. if an event card comes along which makes a players attribute go into negative when the majority of control regions have a negative for that same aspect, then it will be too powerful for the player that received the favourable (usually unfavourable I imagine) event card.

3) Playtest? I cant imagine.

4) See 2) and... a different option would be to make sure that no aspect could have a negative majority in any aspect. This could be achieved by ensuring there were no more than three control equation cards with a negative in any one aspect. Since there are six regions, in this way, it would be impossible to have majority negative for any aspect.

More generally though, it depends what actually works when you play it. You may like to consider allowing a player to reduce an aspect but not make it negative...

If I dont appear to have understood the mechanism, then i hope there is at least food for thought.

Keep it all positive and have thresholds of a fixed number of other things.

Say 12 or higher - or 6 or lower - or odd/even. Simpler is better.

Sounds a bit like El Grande, and quite an intresting mechanic, however I agree that it would be hard to make it intuitive and even more to make it "click".

May thoughts;

Create an overall strategy to pursue for player, i.e. let them focus on one aspect, for example A, B or C.
To add variety they should be able to mix them,
i.e. A and a little bit of C, and to change them during gameplay might the need arise, but having one clear goal an path to follow will certainly help people to get more into the game.

Further, I think it would be cool if regions are inter-connected with each other and respond to each other.
For example a region with a strong bias to A lifts the A part of adjacents regions. Or A kind inhabitans of a region with an A negative will "flee" to adjacents regions where A is positive etc..
So ak kind of pull/push connection between the regions.

This way you can allow for players to "control" regions and receive benefits of them as they pursue a certain strategy.

Hope I was usefull to you.