Use of the word "that" in formal tone, technical writing

In both cases, that is the That-Complementizer, a marker for a tensed Noun Clause, or Complement.

In the first case, both that's are proper, since the repetition marks the two tensed complements that are conjoined by and, thus avoiding ambiguity, which is always a problem in a clause like this.

In the second case, the construction so Adj that S/such a NP that S uses the same complementizer that to mark the complement clause.

That complementizers can be deleted if they are obvious, as in sentences like

• She thinks (that) Mary likes him.
• I'm so tired (that) I can't sleep.

but not if they mark a subject complement and come first in a sentence

• That he arrived late is really his own fault.
• *He arrived late is really his own fault.

because the complementizer is needed as a flag to parse the clause.

However, the longer a sentence is, and the more grammatical complexities it has, the more it is usually not a good idea for a writer to delete every marker (article, preposition, pronoun, complementizer, etc.) that one can, just because it is possible.

Generally there is a function that these markers serve, to clarify a sentence, and one should always be aware that they're potentially there, whether one deletes them or not. Putting them back in is the first thing that a writer should do when a sentence is getting troublesome.

I think it is largely a matter of taste that you prefer the former.

That said, in formal writing especially, including that is advisable. It elucidates the fact that an entire phrase, rather than a single noun, is to be the subject of the preceding verb. This distinction is usually clear with or without that in informal English, and including it may even seem verbose; but in more technical English, with more complex sentences and relationships between phrases, its inclusion helps the reader scan the text. It's more precise.

In the examples you gave though, I can't see a strong preference for one or the other (other than stylistic preferences), as both forms are perfectly unambiguous.

Marine biologists at the University of Utah examined the louse genes and determined their hosts ...

The meaning is clear even at this point in the sentence, as their hosts would not be a noun subject of determined in this context.

During the winter months (July–October), southern right whales come so close to the shoreline, visitors ...

Again, the meaning is clear, because of so implies a subordinate phrase to follow. (So close? How close?)