This is a common misconception where ion concentrations and charge concentrations get confused.

Although the resting potential makes it sound like there is more "positive charge" outside than inside a cell, that difference is really really tiny, we are talking about a tiny tiny fraction of the number of ions in a cell (see for example Why is it possible to calculate the equilibrium potential of an ion using the Nernst equation from empirical measurements in the cell at rest?). For all intents and purposes, the concentration of positive and negative ions are the same inside and outside the cell, to several decimal points.

If someone says the sodium concentration outside the cell changes they don't really mean just sodium ions, they mean sodium ions plus some equivalent number of negative ions. We can ignore those negative ions if they don't have any membrane permeability (see the Goldman equation: ions with no permeability don't count at all for membrane potential).

So in your question you already identified why extracellular sodium concentration doesn't matter much: its permeability is low and the extracelullar sodium concentration is already high. You should not think about adding extracellular sodium changing the charge of ions outside, you should only think about it as changing the driving force for sodium. The resting membrane potential is then a function of a sum of all those driving forces weighted by their permeabilities and calculated with the Goldman equation.

I won't do the math here, but if you actually were able to dump a bucket of just sodium ions, all with positive charge, in the environment outside the cell without a corresponding negative ion in solution, you would create something like lightning traveling at the speed of light and release enough heat to boil your apparatus.

This is a common misconception where ion concentrations and charge concentrations get confused.

Although the resting potential makes it sound like there is more "positive charge" outside than inside a cell, that difference is really really tiny, we are talking about a tiny tiny fraction of the number of ions in a cell (see for example Why is it possible to calculate the equilibrium potential of an ion using the Nernst equation from empirical measurements in the cell at rest?). For all intents and purposes, the sum charge of positive and negative ions is neutral both inside and outside the cell, to several decimal points.

If someone says the sodium concentration outside the cell changes they don't really mean just sodium ions, they mean sodium ions plus some equivalent number of negative ions. We can ignore those negative ions if they don't have any membrane permeability (see the Goldman equation: ions with no permeability don't count at all for membrane potential).

So in your question you already identified why extracellular sodium concentration doesn't matter much: its permeability is low and the extracelullar sodium concentration is already high. You should not think about adding extracellular sodium changing the charge of ions outside, you should only think about it as changing the driving force for sodium. The resting membrane potential is then a function of a sum of all those driving forces weighted by their permeabilities and calculated with the Goldman equation.

I won't do the math here, but if you actually were able to dump a bucket of just sodium ions, all with positive charge, in the environment outside the cell without a corresponding negative ion in solution, you would create something like lightning traveling at the speed of light and release enough heat to boil your apparatus.