I've finished reading Spacetime Physics, and have just a few more notes from the last section of the book...
Momenergy is an awesome concept! The combined momentum-energy 4-vector is very neat. The way that Newtonian energy is just a Taylor expansion term of the full relativistic time component of momenergy is surprising and wonderful. Mass (described elsewhere as rest mass) as an invariant quantity, like subjective/proper time is super-neat. Photons lack mass but still have energy and momentum, as the Lorentzian metric length is zero but the components are not - we have an answer to the question "what happens to the momentum of a particle, when you take the mass to zero and the speed to c?".
Basic particle physics interactions then become... almost obvious. The total sum of the 4 vectors in the system are preserved, and it all flows from there.
One of the nuttiest things is that mass, being the length of a 4 vector, doesn't sum (using the Taylor and Wheeler approach of mass as 'rest mass', not 'relativistic mass'). Unsurprisingly, Taylor and Wheeler avoid trying to build concepts like forces and centre of mass on top of this.
A thing that confused me for a while is that a change of reference frame produces Doppler shift on photons, changing their energy. But... their mass and speed stay the same across all reference frames. What's going on? So, the mass stays the same (0), and speed stays the same (c). With a change of reference frame, both energy and momentum change by the same amount, so that mass remains the same, and it's all fine.
So, I've done special relativity. The last chapter of the book concerns general relativity, and it really leaves me with more questions than answers. Why gravity in particular is a special force, and exactly how curving spacetime is fundamentally different from a field-based approach are not clear to me. On to the general relativity texts, I guess.