Mass is invariant under Lorentz transformation if we consider proper mass (rest mass).
Of course, at rest there is no relative motion and the Lorentz factor degenerates to 1.
The concept of relativistic mass is obsolete and is no longer even taught.
These are merely contemporary trends in physics.
If variant mass is not currently fashionable as the reason for the inability to accelerate it past c, then what is ?
You have only two ways out of this question, i.e. length (space) contraction and time dilation. If you use any of them, I will counter that with the dimensional definition of mass in terms of space and time.
I don't see what this remark adds.
It emphasizes that motion alters the measurements of space, time and mass (charge too, btw).
Potential or kinetic energy, for example, has no intrinsic reality, no location, unlike mass.
Reality is in the eye of the beholder, just like color. Later, I will argue that this applies to space, too.
If the prerequisite for the realness is "location" in Minkowski's space then the relativity of space will throw a monkey wrench into this condition.
It is a potentiality that can be exploited in one system by depleting another, and this is where the question of the reference frame takes on its full meaning, unlike in the case of mass.
Seems like you are distinguishing energy as an idea and mass as an object. ...and you attempt to list some of their properties. I was in the same place mentally 30 years ago and I still think that energy is not an object. Since then I have understood that many other phenomena are just ideas / abstractions. I will agree that color, space, time, force fields and energy, etc... are just ideas - not objects. This will lead us to an interesting question whether compound ideas can become objects, in other words: if something can be expressed solely in terms of these ideas, can that something be considered an object ?
Another interesting question is whether ideas can have properties ...or do properties exist only in the realm of objects (such as the temperature of water) ?
If space has properties such as geometric dimensionality, curvature and "locations" (which you have mentioned), does that mean that space is an object or an idea (like a geometric reference system) ?
As a farewell task, I would like you to consider the dimensions of energy and mass in terms of other concepts.
In English language the word "dimension" has several meanings. One is geometrical, others are not.
In this case I am referring to dimensional analysis of concepts, e.g.:
speed = s/t
acceleration = s/t^2
volumetric flow = s^3/t
etc...
...and please do not come back quoting the SI system's fundamental units for energy and mass, That would be axiomatically boring and dogmatic and will not lead to the expansion of knowledge and understanding.