As to reading texts. I think that there is much too much background echo for most students of NT texts. That is, they are hearing/thinking of the understanding of a NT text from prior knowledge rather than the Greek network itself and the new network is only slowly and imperfectly built if the student simply reads and rereads NT texts. The same thing happens when students look up words in dictionaries. They receive a gloss in another language and typically work with those glosses in the other language network, thinking that that is "Greek," rather than building a new network.
I would give the same advice for non-English speakers who wanted to learn to read the GoodNews Bible or NIV, or [your favorite]EnglishNT. Rereading the NIV is not the best or fastest or fullest way into reading the NIV within a truly English network.
It occurs to me that this is very similar to what happens when you come across cognates while learning another language. Initially, you can't help but think about the word in terms of what it means and how it is used in your first language, and you project that imperfect knowledge onto your second language.
For speakers who don't go on to develop fluency in the 2nd language, these imperfections become fossilized and may or may not hamper communication or cause the speaker to be recognized as having an accent/dialect difference. E.g. Insignificant things like British English speakers talking about using the 'toilet', where Americas prefer 'restroom'. Or more serious errors where English learners of Spanish say "embarazada" to mean "embarassed", but in Spanish this is a false cognate and means "pregnant" instead.
But for speakers who continue to spend time learning the language, and who pay attention to what they're reading (or the conversations they're having), over time, language accommodation happens, and they gradually learn to use those cognates appropriately within the 2nd language's typical usage patterns. They continue to become more fluent speakers of the language.
It seems to me the same should be able to happen with modern learners of Koine Greek. If they initially learn the language by way of lots of cognates (in this case, the cognates aren't just words, but phrases or sentences or discourse-level content), they get a leg up on the gist of the communicative content of the text, but it comes with 1st language bias baggage as well. But over time, by reading lots of koine Greek, including plenty of unfamiliar passages
, learners will self-correct their understanding and replace their original assumptions with new ones that match the actual Greek usage.
I'll readily admit that this requires taking a long-view of language learning, though. "Learning Greek in 1-2 years of typical academic classes" and stopping there will result in students with fossilized & fragmented knowledge of the language. If they haven't been adequately taught how to continue developing their Greek skills on their own, this 'background of English translations' remains a strong influence.