Salamun Alaikum.
I have shared my humble perspective in parts.
The Recitation:
The Quran is a 'mutawwatir' (with majority consensus) reading and secondly a text. Both have worked in tandem to protect the authenticity of the Quran. (recitation + codex). Any codex text of the Quran must always be understood in light of the Quran's mutawwatir recitation.
The main drive of verse 3:7 is to cement a believer's approach to the Quran which is to focus on the fundamental over the allegorical, clear over the unclear, substance over the symbolic, explicit over the implicit, and greater over the lesser. Similarly, no lesser reading can ever supersede a majority reading.
The majority reading of 3:7 without doubt, accepts the pause separating it from 'wa-rasikuhuna fi-l'ilmi' (And those firm in knowledge)
Grasping Profundities:
I think there is a crucial difference in the 'tadabbur' (reflecting, studying, analysing) of clear verses of the Quran, reconciling them with other passages to 'grasp the full profundities' of its meaning, extracting 'hikmah' (wisdom) and applying them to our daily lives with that of 'searching the Quran for hidden meanings' and pursuing 'mutashibihaat'.
There is a difference.
The Quran calls itself 'clear bayyin', so the idea of pondering to extract hidden meanings does not even arise. Furthermore, the Quran clearly rebukes the approach without a proviso. I read the 'ib'tigha 'lfitna' (seeking discord) as a confirmation of a condition along with 'ibtighaa tawilihi' (seeking its interpretation) not a proviso. As with 74:31, there is a disease in the heart (fi qulubihim maradun) which makes them take this approach.
In my humble opinion, such an approach to seek hidden meanings and to justify it from the Quran is usually concocted by those that largely have a theological axe to grind to support esoteric knowledge and twist clear verses of the Quran to support a particular theological bias.
I hope that helps, God willing.
Regards,
Joseph.