Since he is 6 mo, is he on solids? Trying pear juice or prunes for the hard stools I think would be acceptable now unless he has food intolerances then you would want to go another route.
Neocate tastes horrible so switch slowly (an oz per bottle a day or something like that) to let his body get used to it.
It will not help with the spitting, but I noticed you did say your doc wanted you to add cereal. That should help keep it down better. But if he’s not screaming with the spitting because he is in pain, the spitting will resolve itself later. Reflux also peaks about this age and so it could be just a bad phase.
The stools will be dark in color and that is normal, I would say Neocate made my son constipated at first until he got used to it and we used 1/2 jar of prunes every day or every other. He had blowouts sometimes if we did it every day.