A true synthesis of the Left and Right in politics would be something like fascism: Right Wing cultural sentiment implimented coercively through the violence of Left Wing mechanics.
That, or it would be Libertarianism: classically Right Wing economics with the Left Wing proggressive over-determination of mankind's unquestionably equal agency in the face of the free market (a secular stand-in for Free Will).
The real Center would not be a synthesis, but rather, something politically akin to the 'middle path' referred to in the far east. In spiritual terms, one could say this is a position which recognizes being as superior to effects or to becoming. It centers the attention of the subject so that it may always remain in balance. To balance, one needs something to balance between.
This could, perhaps, only be accomplished through an attitude of apoliteia, ironically. Life itself must become the issue, not ideologies or means of adequately predicting the economy.
For this to be an option, society would be designed in such a way that people would be encouraged to strive for the highest agency they could, thus managing their own lives, putting them in agreement with others who want the same.
The impulses which created the Left and the Right are far older than either. Both have their uses, but the modern world sees both as only able to exist at the expense of one another.
In a culture where everyone is encouraged to maximize agency over themselves, it is more likely that people will be able to freely associate, thus being able to develop whatever kind of organization and economy that suits them best.