The convention for converting an originally present-tense direct-speech utterance to a past-tense report (indirect speech) is that the present-tense verb in the original is 'backshifted' to past tense.
Fred insisted "I **will** be driving my car in the rally.
⇓
Fred insisted that he **would** be driving his car in the rally.
As you correctly discern, a reconversion from indirect to direct speech simply undoes this change.
In your Alcatraz sentence the tensed verb is simple present look; consequently, the indirect-speech version should employ a simple past:
The officer said, “They **look** like fugitives from Alcatraz.”
⇓
The officer said that they **looked** like fugitives from Alcatraz.
You would employ past perfect only if the original employed present perfect.
The officer said, “They **have** been transported to the hospital”
⇓
The officer said that they **had** been transported to the hospital.
Mariko would have never gone through with the wedding, not once the
will was revealed.
Mariko would never have gotten married--not after the will had been revealed.
When the contents of the will were revealed, Mariko had a reason to not get married.
To go through with something means to actually do it, to see it from start to finish, to complete something that is planned or contemplated.
He threatened me, but I knew he would not go through with it.
Once, in that sentence about Mariko, could be translated "immediately after". It refers to a situation that "comes-to-be-as-of-that-moment". "The very moment that..." or "as soon as".
Once I saw that look in her eyes, I knew it was she who had killed the cook.
Once he heard her goose-like laugh, he knew they could not spend a life together.
You cannot change your mind after leaping from a cliff. Once you've jumped, you've jumped.
Best Answer
Though without the use of "that" the sense can well be imagined, we are very much inclined to retaining the same as the question is about narration change and that too with back shifting.
Barring exceptional exceptions, if the reporting speech is in past tense, the reported speech should be in the "corresponding past tense" of the tense used in direct speech.
Let us scrutinize the direct speech. It could be seen that except 'driving of the car' every thing else is shifted back. Alright. We would distance the "driving" farther by using Past Perfect Continuous Tense( had been driving)
"To have" can function as both principal and auxiliary verb. Not only in indirct speech but also in any demanding situation HAS HAD, HAVE HAD or HAD HAD is used all the white. We can still find in our mind's eye the milkmaid of Dr. Edward Jenner's description moving fearlessly among small pox patients because she HAD HAD Cow pox.
So all we can suggest is to put 'that', first , change ' was' to 'had been' next and retaining ' had had' last. The text is now perfectly balanced.
As regards use of "while", in whatever way we look at it — as a temporal preposition with time related complement clause or a conventional time subordinator(conjunction)for simultaneous activity/ reference to background to the focus-activity in the main clause, there is not much of a difference. We are to use past perfect in both as stated ealier.