1. Should be:

(1pr) Alissa m’échappe sans cesse ; non qu’elle paraisse jamais se dérober

2. I would say:

(2im) Alissa m’échappait sans cesse ; non qu’elle parût jamais se dérober

3. I think indeed the author thought that in the past. Well actually, it is a past tense, isn’t it? I don’t think it says anything about what he thinks now, though.

This one:

Je n’ai pas dit qu’il eût raison.

Sounds funny to me. I would say:

Je n’ai pas dit qu’il avait raison.

This one:

Je n’ai pas dit qu’il ait raison.

IMHO would be (esp. in conversation):

Je n’ai pas dit qu’il a raison.

This one:

Je n’ai pas dit qu’il eût eu raison.

is really “acrobatic”. It might be grammatically correct, but nobody would say that, and maybe it would be rare even in writing. It sounds improbable or pedantic.

This one:

Je n’ai pas dit qu’il ait eu raison.

Maybe works, but I would have said:

Je n’ai pas dit qu’il avait eu raison.

(1pr) Alissa m’échappe sans cesse ; non qu’elle paraisse jamais se dérober

This one is ok because it is Present in the first one and non que has to go with Subjonctif. We use the Present form to indicate a simultaneous or posterior action while the Past Subjonctif would refer to an anterior action.

(1im) Alissa m’échappe sans cesse ; non qu’elle parût jamais se dérober

It is not possible to mix Past Subjonctif with the Present tense in the narrative – Past Subjonctif can only be combined with past tenses

So this is not correct

(2pa) Alissa m’échappait sans cesse ; non qu’elle ait jamais paru jamais se dérober

This one is ok according to the new French grammar standards – non que + Subj and Subjonctif Passé Composé to indicate an action that either happened in the past or has started in the past

(2im) Alissa m’échappait sans cesse ; non qu’elle parût jamais se dérober

Correct – Subjonctif for non que and Subjonctif Imparfait for a simultaneous
action

Verbs of statement such as dire, exprimer, etc do not require Subjonctif – the que clause you are referring to there is called conjonctive or completive and it performs as a COD ergo not requiring Subjonctif

These two sentences:

Je ne dis pas qu’il ait raison. (I don’t say that he is right.)

Je n’ai pas dit qu’il eût raison. (I didn’t say he was right.)

are not correct as dire cannot have Subjonctif – it only demands back-shift for the second one.

Je n’ai pas dit qu’il avait raison. – simultaneous – I did not say he was right.

Je n’ai pas dit qu’il avait eu raison. – anterior – I did not say he had been right.