"I want the gallery organised so I can see a smooth transition in style from the more peaceable Mecca period through to the less peaceable Medina period."
the thing is that, makkan or madinan chapters are classified according to where the opening verses were revealed, even if later verses were sent down whilst Muhammad pbuh was in the other city.
www.quran-institute.org/articles/makkan-and-madinan-revelations
so even for people who wish to delineate the peace verses of the Quran as historical anomalies because they consider the later war verses of the Quran the real face of Islam. saying the organisation of their reading is for chronology is not accurate at all. you would need to know which verses were makkan or madinan, not just which chapters if you wanted to know the historical context.
I myself like to know which verses are referring to which events in the life of the Prophet Muhammad pbuh, and it is nice to explain them according to his own life events in order.
but I can see that the people who would consider chronology as starting from the beginning of time, to each prophet in order of their chaplaincies, to ending with Muhammad pbuh lifetime, those people also have the right of it.
there isnt any right way or wrong way as you said outwith. it depends on the reader's perspective coloured by their own background and preferences.
And in actual fact the chapters dealing with war tend to be large and are found near the beginning of the Quran so someone reading from the first page as the OP would find them pretty soon anyway. they're not hidden deep in the middle or the end.
some consider the Makkan and madinan periods as like the difference between the Old Testament and New Testament where the latter abrogated the former. whereas the Quran is one single book. It is not multiple gospels or the works of different prophets brought together as the Bible compiles what we consider as the Torah, the Zabur and the Injeel: (the books of Moses, David and Jesus). the same themes come up throughout the Quran and to muslims its a coherent, consistent, unified literary work not two separate works which is why the focus is not on which chapters are from which period.
in fact to ordinary muslims the makkan period was v crucial for laying down the theory and spirituality of the religion, the history of monotheism, islam's place in it, the creation of our religious identity. (that's why we start children on the short chapters found at the end of the Quran and work our way in from that direction.)
whereas the madinan chapters are about the structures, the rigours, the rules of the faith. wash arms this way, don't eat meat from ....., walk like this, don't talk like that etc..... laying down islam's orthopraxy. we cannot dismiss the makkan chapters because without the faith and explanation of religion laid down in those chapters the madinan chapters would be merely rules and regulations with no faith underpinning. so theyre significant far beyond a binary understanding of war and peace. Good luck with your readings.