So I was pleased to stumble across "Medieval Warfare: A History" ed. Maurice Keen, in a bibliography elsewhere, and discover it in my local public library.
Thought: DO use your public library to sample books before you spend $$ on them at Amazon - it never hurts to figure out if a book is genuinely worth having or not and the gaming budget can be saved or spent elsewhere!
This book is pretty recent, from 1999, and has a series of articles brought together by scholars across the field. I read through a couple of the articles that were in periods or on topics with which I'm familiar and have read other authors, and these seem like very reasonable overviews. In other words, the generalizations and conclusions seem to be well-informed, neither the work of a young author who is just trying to cause a stir, nor a jaded old geezer who is careless or dated in his scholarship.
The "phases" are more like "eras and areas" of medieval warfare. As both geography and culture impact warfare, I found it useful to have the book organized thus.
The "further reading" section is excellent - organized by topics such as naval warfare and military orders or by geographic areas. Worth take a pic of and keeping for future use! The Chronology also helps give a big picture and a grasp of sequential developments.
I hope you're able to find this, but if not it seems pretty available at Amazon for about $6 + $4 shipping, so $10. I think I can recommend it heartily for anyone interested in gaming this period, either a newbie or a veteran.
