Dear Chris,
You observe that Einstein "tells us that there can be no simultaneous measurements between different frames of reference." This is of course based on his 4D ontology in which he assigns a universal time dimension to every frame. There's recent evidence that the 'time dilation' (= clock slowing) of 4D special relativity space-time theory can be explained quite simply in a (3+1)D-ontology formulated in terms of energy-time.
This is compatible with the Global Positioning System (GPS) where clocks are adjusted to compensate for the kinetic energy and gravitational energy of each clock and effectively establish the universal simultaneity that our commerce is based on.
I very much like your treatment of "unstated, and imaginary, frames of reference" in 'The Liar's Paradox'.
You continue to unearth such 'unstated frames of reference' as you go through a list of paradoxes. This is a fruitful enterprise for you; I'm unsure how it translates to ontology, i.e. reality.
In special relativity all paradoxes are associated with Einstein's 4D-ontology and disappear in (3+1)D-ontology. You might find my essay Deciding on the nature of time and space that touches on this to be of interest.
I was looking forward to the General Relativity mentioned in your title, but was hoping for more in your slight treatment of this.
In general, Einstein defined a 'simultaneity detector' as operating at the midpoint between two distant simultaneous events. Obviously only the detectors on a bisecting plane can register such events as simultaneous, but in (3+1)D-ontology, simultaneous events are simultaneous, regardless of whether that news reaches all observers at the same time.
A very interesting essay -- good luck in the contest.
Edwin Eugene Klingman