I tend to think if you can't explain something to a toddler, you don't understand it. Just so happens I'm trying to figure out the 'explanation' of Lorentz transformations at www.emmynoether.com
I found it useful to take the approach of drawing graphs and making sure each step is very visible; no tricks, no fudging, no obfuscation etc.
So far haven't fully figured out what they are saying after I found an apparant blatant error which may be explainable by something else they said.
However, I have found a way of analysing things which may explain a lot.
My view at this stage tends towards:
"Time" is a figment of the imagination. It may help to write it out of physics equations and replace it with what is really being refered to.
All "time" concepts actually involve "reference space"; eg. a clock is just a movement in "reference space".
Lorentz transformations should be re-worked as the relationship between 3 patterns, using 6 graphs: (Maybe use a 4th, with 2 graphs, for 'c')
POSITION IN SPACE: A first-position-of object graph; A second-position-of object graph;
REFERENCE POSITION IN SPACE: (call 'time' if you like)
A first reference-position of reference-object graph; A second reference-position of reference-object graph
SECOND REFERENCE POSITION IN SPACE: (call 'relative movement between object and an observer's frame-of-6-graphs') A first 2nd-reference position in space graph; A second 2nd-reference position-in-space graph
Note: This fits my general analytical system: 3-way-jump theory! Also involves 'local gauge invariance': you can set your gauge to zero anywhere as what counts is 'the difference' between patterns A and B seen by C, or difference of C and A, seen by B; or difference of B and C, seen by A.
Incidentally, I started properly mapping 3-way jump theory; and got amazing patterns; including ones reminiscent of DNA!