Woodward wrote 'Woodward on Time' (WOT) which is excellent. However; I don't have 'My Own Right Time' (MORT) and suspect there is some overlap. WOT contains all of Woodward's articles, mostly published in the Horological Journal (monthly journal of the British Horological Journal). You will find much of interest at the level you seek, in the BHI Journal. Membership is not cheap, and the Journal does not have a huge number of pages (about 44 pages per issue), however; it is the place where you will find the most relevant information and articles, both practical and theoretical (reflecting the craft/theory balance typical of the way horology has developed.
The USA-based National Association of Watch and Clock Collectors (NAWCC) are worth a look, but once a member you may also opt into the Horological Science Newsletter, which will more than satisfy any desire you might have to delve into theory. I have found them to be an excellent and very helpful source.
There are lots of books dealing in a serious manner with particular aspects of clocks and watches; and some of those contain some theory. Many contain an in-depth review of a particular kind of clock, and some contain associated musing s on the theory. There are also lots which review types of clocks but do not delve into theory at all. All are expensive (a trait of horological publications of any size).
I believe the craft/theory balance is represented by Wilding and Woodward. John Wildings books are tremendous if you want to make a clock but are not bothered by theory; while Woodward never intended to be a maker, but was interested in the theory. Both have helped take us forward, and both are necessary components in the development of theory. That craft-then-theory path represents fairly typically the way horology has developed since its beginnings. I do believe, though, that the subtle underlying physics are just that – subtle- and most people looking at, or even repairing a clock or watch do not fully appreciate the influence of physics on the physical article, or the theory brought into action in a clock. That's not just true in horology, of course.
Woodward's most important practical work, based on theory, was W5, an impressively accurate clock completed in 1985, and detailed in MORT, I believe. WOT contains a chapter entitled 'A Fresh Look At W5' (first published in Horological Science Newsletter). There has been a lot of interest in that clock, and the underlying theory, and it has been subject to some important development, since the WOT book.
One or two other titles from my bookshelf:
The Science of Clocks and Watches (Rawlings)
Clock and Watch Escapements (Gazeley)
Wheel and Pinion Cutting in Horology (Wild)
One of the conundrums is that early pioneers understood, at least partially, what they were doing, but did not develop the physics or spread the knowledge. The craftsamn protected his own key knowledge, perhpas? That means later studies of the development of particular types of clocks represent an attempt to trace, reveal, and understand the early knowledge (a kind of knowledge archeology perhpas). So there are interesting strands of theory in many of the serious horological books on particlat clocks. Synchronome, by Miles, for example, survays the life and works of Synchronome and his clocks, but also contains clear and well expressed explanations of the theory and practical realisation on which the clocks are based. So a further list perhpas depends on the kind of clock in which you are interested.
I have those kinds of books on Synchronome, longcase, precision pendulum, chronomoeter, musical and electric clocks, which suggests I am interested in the pure mechanics and physics in all clocks and watches, which seems about right. That's the spot that Woodward hits. MORT and WOT being the top of that pile.
Marcus