Joules, ergs, foot-pounds, electron volts, take you're pick.
It looks like you're trying to make a point, just make it.
Yes this would take a lot of questions. But it is hard to get to to answer anything but extremely simple questions without you flying off on a mythical wave aether tangent.
I will try and condense this down to a simple idea for you.
1) c is not really defined by light. It was discovered through the study of light. Neutrinos also travel at c. If gravitons exist they also travel at c. c is really the maximum velocity of anything. Photons are not specifically needed in its definition.
2) In your luminiferous aether / wave aether idea, you have made some pretty bold claims.
a) The wave aether and photons cause physics to exist.
b) The wave aether causes space and time to exist.
a) is too problematic to address. It is vague and crank-like. Like many things you say it is a swiss cheese of logic.
b) if aether causes space and time to exist, then it must be beyond space and time. It is nowhere and no-when. That is the definition of non-existance. Just because you can make a statement does not mean that it is true or even logical. As far as ontology goes, it has no place in physics. Questions of being and nothingness have no place in science. Your claim that aether is a required for ontology has no logical basis. The one place that physics deals with ontology is the Big Bang and the ontology part of that has not been very successful (though the theory as a whole is very successful).
Finally, in the formula, E=mc^2, if you trace the derivation back, c is part of gamma, a dimensionless number. The formula E=mc^2 is generic and so it's constructed units can be joules, ergs, or whatever. I picked joules because it is the most common unit, and it has no velocity in it's definition. An exception breaks the rule. I could have written m=E/c^2 where the central idea is mass, which also has no velocity definition except in relativity through gamma. Normally mass is just mass. Or I could have written, 1=mc^2/E, a unitless number where c also relates to gamma. But 1 has no built in concept of velocity. No units at all. It is just 1 with no units, but the formula does mention c. You can plug E, m and c into the formula and 1 will pop out. The left hand side of the equation sets the units we are interested in. (and yes, I know the units on the right hand side cancels, but mass, energy and c are still there on the right hand side, otherwise I would have written 1=1).
Side note, I have watched those Susskind videos 2X, and similar classes from MIT and other places.
So now I imagine your mind has drifted off and is blissfully in wave aether land. All what I said here is wiped clear and a smile has appeared on your face.