You seem to want to avoid it so let me pull the LS rubbish apart
Gravity affects everything that exists equally regardless of mass and this includes massless particles.
WRONG under no physics framework does gravity directly effect massless particles. Gravity lensing is an indirect effect but he makes it quite clear he believes it is a direct effect.
For LS is we fire a bullet and a laser horizontally along the same path they are both effected by gravity and slowly bend down until they hit the ground. Have you ever seen a laser beam do that because I sure haven't. Perhaps he should talk to Marosz.
Both Newton and Galileo understood this centuries ago, even though relativists claim that they are the ones who figured it out. Go figure.
So no they didn't and nor do any relativists say that and LS is completely wrong ... GO FIGURE
The problem is that this undeniable principle means that gravity also affect gravitational waves.
Oh now its an undeniable principle ... so a completely wrong thing is undeniable and its going to effect gravitational waves.
Since these waves affect themselves, they either cancel themselves out or amplify themselves recursively.
What is he even talking about???? My best guess is saying they interfere constructively and destructively like a wave in a media and I can only assume he has got gravity wave and gravitational wave mixed up.
The same objection applies to so-called curved space and to hypothetical intermediary particles such as gravitons. In other words, if it exists, regardless of its mass, gravity affects it. The infinite self-referential regress is too painful to even contemplate.
The self interaction part is correct we have discussed that before and it is not too painful to contemplate it creates the concept that space must have a pressure to oppose the runaway, something we have discussed.
Now dealing with your later posts your discussion of Einstein is pretty much correct. For all his brilliance he liked his classical world and struggled with what his own theories actually said.
Then finally you say mathematical equivalence is no guarantee of physical reality. Well that is a loaded statement and you need to explain what you mean? Perhaps if you could prove to me the other 3 dimensions exist so I get how your proof is based.
In mathematics if things can not be simplified from 4 dimensions down to 3 then the 4th dimension exists regardless of what you believe. The question of dimensionality is about simplification and concurrent access of phsyics quantities not what you believe or think reality is. You would end up saying to me I don't consider that a dimension it doesn't look like one and I would probably burst into laughter.