Not having read the whole thread i will comment on OP.
It is not clear what you mean by Jhana and if you are familiar with the Theravadin Abhidhamma classification of states that are good in regards to the word ‘jhana’. Therefore i won’t get into it.
In general this is how i train to develop insight and other states that are good;)
I develop mindfulness of breathing thus; https://docs.google.com/document/d/1hRy-g6o8yKsDQnR6_sbBbY5ZVpDbQ5-_LURXqwxS7YU
as for ‘Insight’ it is also not clear what exactly you mean, i will assume that you mean something like (from Abhidhamma); That which is wisdom, knowing, investigation, deep investigation, investigation of (the nature of) things, discernment, discrimination, differentiation, erudition, skilfulness, subtlety, clarification, thoughtfulness, consideration, breadth, intelligence, guidance, insight, full awareness, examination, wisdom, the Faculty of Wisdom, the Strength of Wisdom, the sword of wisdom, height of wisdom, light of wisdom, lustre of wisdom, flame of wisdom, treasure of wisdom, non-delusion, investigation of (the nature of) things, right view.
For development of this i contemplate thus; https://docs.google.com/document/d/1kZxstsAvjhj9Svc47RUKRIyKQMuHMD4adIvr_7pp2uI
At times i do contemplate during Anapanasati as well, primarly focusing on inconstancy and the 4th tetrad of the standard Anapanasati instruction.
In general i try to adapt the training to what is appropriate, sometimes i have to drop a theme because i can’t rouse the mind with it and mind is unyielding to that particular development so i will try contemplating something else or rouse the mind otherwise, in general i follow this outline for timely & untimely development; https://docs.google.com/document/d/18b57EkdwyqsmER1dS5MPqpeWSjj82A7qvqYlXrhkCPQ/
I think the anecdotal books on Anapanasati like those of Ledi Sayadaw and Leigh Brasington are quite useful primarily if one wants to develop concentration leading to the pleasant abidings by tranquilizing the breath.
When signs/sensations do manifest i recommend Upakilesa Sutta and Leigh Brasington’s instruction on how to react or not to react to those phenomena. I am not an expert so make your own experiments:)
ps; the docs are my own notes, primarily meant for personal use, therefore presentation and content might be disagreeable to others.