Interesting reading. I would like to comment about a couple of things to think about.
...a finding that is in keeping with the absence of a carotid sinus in the giraffe.
Does the giraffe have baroreceptors? There has to be a way for an erect animal to regulate cardiac output via stroke volume, heart rate, etc.
...The viscosity of giraffe blood was found to be 4.9 times that of water; the erythrocyte count 11,950,000) per m) was similar to that of the camel and llama and double that of man, indicating a greater oxygen carrying capacity.
Viscosity of blood can only reach so high a value before sludging occurs. This assumes normal clotting mechanisms etc which may not be the case for sauropods. However, it is likely to be so. Also, the oxygen carrying capacity of blood is dependent on oxygen concentration which would be ambient for dinosaurs at 21% or so (an assumption) and pH primarily. Under normal circumstances O2 saturation is around 90+%. No more oxygen can be delivered to the cells by increasing O2 concentration in blood unless you increase the barometric pressure. The greater number of erythrocytes would allow greater oxygen delivery at the cellular level. Peruvian Indians are dwarfish with very large barrel chests and purplish ears and lips. This is due to high hemoglobin/hematocrit/erythrocyte levels. The above assumes normal hemoglobin O2 carrying capabilities for dinosaurs.
...To pump blood 12m from the thorax to the top of the head the heart of Barosarus would need to achieve a systolic pressure of 12,000 mm of water, or about 880 mm Hg. Such an enormous pressure would require a very large and strong heart and very thick walls in the arterial system to prevent rupture, Indeed, zoologist Roger Seymour (cited by Lillywhite) estimated the heart size of large saurorpods to have been more than 1.6 metric tonnes, or eight times that of a whale of similar size.
The heart is not the only mechanism for pumping blood. The heart/lung/thorax/entire circulatory system is responsible. Compression of the ribs and hence cardiothorax increases CO much greater than one would anticipate with mere manual compression of the heart. Plus the circulatory system is a closed system. There is inertia and fluid dynamics involved. Also the aorta pulses and increases cardiac output lessening the work of the heart. I would imagine the heart occupying a certain proportion of the thorax along with the lungs. I would keep things proportional but this is just an opinion.
...We have already postulated that the cerebral arteries would have had check valves to lighten the load on the pumping mechanism. Perhaps there were multiple pumps, in series so that the primary pump (heart) would have had to generate only sufficient pressure to drive the fluid column to the next pump, and so on. How many pump relays would there have been? If the heart produced a systolic pressure of, say, 200 mg Hg, five pump levels would have been needed, We postulate that the cardiovascular system of Barosaurus consisted of single primary and secondary hearts and three pairs of hearts in series, each being 2.44 m higher than the one below The primary heart would be in the thorax. The second heart would be in the thoracic inlet. The next three pairs of hearts would be smaller and situated in the neck in the openings lateral to the spinal cord. With the exception of the first heart, all the hearts would be singlechambered, with valves located at the inlet and outlet of the aortic trunk.
This is very interesting but would require an evolutionary divergence of great proportions which is of course possible. However, I would point out that check valves and extra hearts are not entirely necessary. What is required absolutely is either a very strong aortic valve to prevent blood from entering back into the left ventricle (assuming a four chambered heart) or an anatomical kink in the aorta which I find unlikely due to hemodynamics.
...To generate 880 mm Hg pressure, the Barosaurus heart would have had to be very large and very powerful, and it would have had to beat very slowly because of its size. With a long diastolic interval, there would have had to be check valves in the neck arteries supplying the brain (the two cerebral arteries in reptiles) to prevent the column of blood from falling back to the heart during diastole.
This may be true but it assumes that the heart would not be able to increase CO without increasing ejection fraction via more vigorous contractions. A large heart would still be able to beat at higher rates IMO as well. Normally right ventricular function is a byproduct of left ventricular function. The more vigorous the heart beats the greater the return to the right side of the heart hence to the left side. What is the upper limits of normal for the PR interval in a giraffe or large whale?