It sounds like you've got your bases covered with the specialists. It's encouraging that you had a near term and term delivery. Many times PE comes on later and milder in subsequent pregnancies - which might bode well for a third. It is a good idea to rule everything out, but I wouldn't give up hopes of another baby if you really want one. MANY of our members never have diagnosis, but manage to complete their families, especially with a history of near term deliveries. Obviously, there are no promises. Some have finally gotten a diagnosis of something after 3 pregnancies. Some might get a diagnosis later in life. I was going to suggest getting acquired clotting disorders rechecked, but with deliveries past 34 weeks, clotting disorders are less likely a culprit. It could be something like Chronic Fatigue or Fibromylagia for which there aren't definitive lab tests, but only clinical symptoms such as fatigue and pain.
Let us know what happens with your appointments.