You're trying to get the tenses of "had" and "was" to agree. Don't. They can't. The tenses interfere with each other, even when they are both in the same tense. The passive infinitive does not have any tense. It doesn't have any desire to have a subject all to itself. It's the verb form that works as an argument of the verb "had".
A separate question for you:
But why that's don't it end as "was being carried"?
Did you mean something like:
But why doesn't that end with "was being carried"?
The first word of the sentence is a conjunction. That's fine in many non-scholastic registers.
The second word of the sentence (really, the first word inside the clause) is the topic of the question. This question can be summed up with the single word "why?"
The word that immediately follows the question's topic is the first word of the question's complete verb.
The "that" is the subject, referring to the subject "the correct ending of the sentence" in a prior clause.
The rest of the sentence is just the rest of the predicate.
What you originally wrote doesn't have the typical word order of a question. The 's of "that's" doesn't seem to have any purpose. The verb form "doesn't" agrees with its singular subject. We have a stray "it" that also doesn't seem to have any purpose. We only need one subject for this sentence, and the word "that" is sufficient.