The Modern Synthesis (1930’s and 40’s) predates the discovery of Neutral theory (1960’s), This would mean biologists abandoned what you describe as Neo-Darwinism about 50 years ago.
That is not an interpretation of data, at least not a scientific one.
The Modern Synthesis has already been heavily modified by Neutral theory. I haven’t seen anything presented by Noble or others that requires a drastic modification of the theory we already have. Yes, there are a few species that pass on methylation patterns to subsequent generations, but these are limited changes and a limited number of species. This doesn’t change the fact that the bulk of eukaryotes do not pass on methylation patterns in any meaningful sense, so the Weismann barrier does apply to many, many species.
This may run into problems when we look at genetic diseases. Some children are born with genetic diseases that are a product of de novo mutations. I think it would be difficult to say that either the parents or the child chose to have that mutation. We also don’t choose to have cancer which are also a product of somatic mutations, and can possibly occur at a higher rate in people carrying other inherited mutations (e.g. BRCA4).
I tend to view the discussions on morality as a question of dualism. Even ignoring evolution for the moment, I think most would agree that the human brain is produced through natural means as part of embryonic development. How that relates to consciousness and brain function is a whole other discussion.
I would agree that the Modern Synthesis as it existed in the 30’s and 40’s is not the best model. The current theory, however, is pretty good. What I would encourage you to do is look at the actual data, not the misrepresentations given by Noble and others.