Kerenshara: Sorry. My post should have been addressed to the OP. Sorry for the confusion.
But by relaxation I mean relaxation of the ventricular wall. This allows the chamber to dilate, allowing increased filling (what we call preload) which primes the heart for a stronger contraction and increases the volume of blood the heart moves with each contraction (the stroke volume).
(As an aside: SV x Heart Rate = Cardiac Output, which is the principle measure of overall cardiac function. The normal resting HR for an adult is 80 to 100 bpm. Lance Armstrong's resting HR is 32-34 bpm but his CO remains the same. That means Lance moves roughly 2.72 times more blood with the same amount of work. Freakish.)
As far as your other ideas, your right and left heart basically are separate, as are your pulmonary and systemic circulations- basically like a parallel circuit. separating them wouldn't make much difference, except that as you stated they would contract independently which would actually be bad for a couple reasons. And thinking about it, I don't think adding a second heart in series with the systemic circulation would really do anything for you. Maybe a second heart in series with the pulmonary circulation would help with oxygenation (tho I'm not sure how it could be much better). You would have to modify the left heart tho, for greatly increased preload. You could put a "venous heart" low in the pelvis that pumps deoxygenated blood from the lower extremities back to the central veins, maybe. Might help reduce lactic acidosis, which plays a big role in muscle fatigue, but who knows.
Probably best not to think about such things.

That way lies madness....