Table Permissions Sanity Check: GRANT not working
Ok, so my broader question still stands (and will likely build that out in its own forum post) but for now, I'll answer the immediate problem here.

My GRANT query was syntactically incorrect and that was producing the error.

My query:

GRANT SELECT,INSERT,UPDATE,DELETE ON "schema1.new_table_name" TO "role1";

Should really be:

GRANT SELECT,INSERT,UPDATE,DELETE ON "schema1"."new_table_name" TO "role1";

(I was missing closing Quote marks after the schema name, and opening quote marks before the table name)