Looks fine to me. I would mention that in more advanced treatments of EM, it is seen the equations more or less follow from gauge symmetry which has its origins in Quantum Mechanics:
https://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html
For those advanced enough, you define the EM tensor Fuv from A, show it is antisymmetric, has six independent components that can be grouped as the 3 component vector E and the three-component vector B. We note ∂u∂vFuv = 0, meaning δvFuv defined as the 4 current Ju can be interpreted as a continuity equation of something we will call charge. Up to now, it has been nothing but math. This is the key physical assumption needed. You have Maxwell's Equations. However, the Lagrangian formalism is needed to derive the Lorentz force law.
The above is quite mathematical. A more physical approach is the following:
https://iopscience.iop.org/article/10.1088/0143-0807/36/6/065036
I do not expect your audience to be advanced enough to understand any of the above. But it could be mentioned justifications exist once more advanced material is understood and handed out as supplementary reading for when they are more advanced. It is of value to see how it all fits together when students are learning the more advanced material. Often it is not part of standard treatments of the tensor formulation of SR, which IMHO is a pity.
For those really keen Lenny Susskind has written an extremely good book, IMHO understandable even by advanced high school students, bringing this all together, including the needed math:
https://www.amazon.com.au/dp/0141985011/
Just a few thoughts some of your more interested students may benefit from.
Thanks
Bill