I think A0′ and A1′ don’t mean exactly what you wish. Reading the sentence alone implies (M will stand for Meursault) :

M imagines what would be his life without her, but it’s not as good as first expected.

Where A1′ has a stronger meaning of “but it’s not”, and talks about his past life.
Whereas A0′ talks about his actual life.

So if the meaning you wish is different from this one, you have to complete the sentence A0′ or have a strong context to make it clear. The fact that M wishes the situation to be true must be clear.

EDIT :
About “he don’t like his life”, this is just an example, to be easier to understand. I removed it so there is no confusion…

About the meaning of A0′ and A1′, the problem is that a sentence can have multiple meaning, depending on the context.
I say that without context, one won’t understand it the way you wish.
So you HAVE to add context to make the meaning clear.
Also, the “but it’s not” is implied by the past tense, because we understand that he doesn’t think so anymore, so that he was wrong. You have to add context to say “I don’t know what he thinks now”.

Just to guide anyone trying to answer the question, I will write a hypothetical answer to show the kind of things I am looking for.

HYPOTHETICAL ANSWER

A0′ correctly expresses the situation described, i.e. Meursault e.g. yesterday thinking his then current life would be better without his mother. It is because French conditionals do not “backshift” exactly the same way English “subjectives” do not. (E.g. “I think it would be better without her.” “I thought it would be better without her.”)

A1′ does not express the situation described. What A1′ express is that Meursault e.g. yesterday thought that his past life, e.g. his childhood, would have been better without his mother.

END OF HYPOTHETICAL ANSWER

I am not saying the answer has to go like the above. It might say the opposite thing, for instance. But I am saying you have to answer the question that was asked. And you have to understand the question. If you’d like, you can even provide an answer by commenting on, denying or affirming, the hypothetical one above.

In the context of a narration, your question is clear and the answer is probably the one you expect:

• (A0′) expresses an opinion about his hypothetical then-current life. (In fact, it could also be about his then-future life).
• (A1′) expresses an opinion about his hypothetical then-past life.

A speaker may avoid the compound tense, but only at the expense of a meaning approximation, relying on the fact that a better past life is generally relevant only to the current/general life.

However notice that this is only true in the case of a standalone sentence in a narration. If you use it as a clause in a bigger sentence, beware that the time referential for the comparison may attach to a different time than the one of “penser”. It becomes a bit complicated, but I think it’s relevant to your question.

(X) Je crois qu’il pensait que sa vie serait mieux sans sa mère.
(X’) Je crois qu’il pensait que sa vie aurait été mieux sans sa mère.

In such cases, because conditional can be used for both present and past, the time referential for “être mieux” can be either the one of “croire” or the one “penser”. In X the time span for “être mieux” could be “from now onwards” (if croire is the referential), or “from then onwards” (if penser is the referencial) onward. Similarly the time span in X’ could be “until now” or “until then”.

The same thing happens if you directly prepend a conjunction, it potentially introduces an additional time referential.

Puisqu’il pensait que sa vie aurait été mieux sans sa mère, […]

In such a sentence the clause that contains the compound tense may match the meaning you are after. Interactions of time referentials can become quite complicated sometimes. These tricky sentences may have different interpretations.