A universe' can mean a collection of people, things, or companies that have similar characteristics or features. Although many people find their own moral code, there are generally recognised 'types' of morality, sometimes characterised by religious or ethical beliefs, or by cultures etc. The word "world" is sometimes used in the same way.
A "moral universe" must refer to a universe of morals, that is a recognised set of morals, and collectively all those who live by it, perhaps also all actions carried out in line with those morals.
The text seems to imply that the character in the story has become involved in people or events that go against his previously held morality, and that he doesn't like it, but does not feel like he can leave it now.
"Seamless logic" is more familiar phrase. Literally speaking, if a piece of clothing or similar is 'seamless' it means either that there are no joins, or that you cannot see the joins (where the material has been sewn together). In a metaphorical sense, the term is used to refer to something which is very well put together so that you cannot find fault in it. For example, when different cuts of film are edited together well so that you cannot see the transitions, it may be described as 'seamless'. 'Seamless logic' would suggest that the logic was so well put together it was coherent and logical.