I don’t think embalmers look inside very much at all. All they have to do is replace the blood and abdominal fluid with the embalming fluid. This is done through needles.
That was my understanding as well. That is why I am having trouble believing embalmers found clots INSIDE veins.
The reason they would be acutely aware of this problem is that they have to pump embalming fluid through the circulatory system, as you said.
These BLOOD CLOTS block the normal flow of blood throughout the system. ERGO, they can’t pump their fluid into the deceased body.
So, they are left no choice but to investigate why, and VOILA !, guess what they find ?