I love the fact that you are trying to make a hybrid muffin which will hopefully give you both the height and healthiness you are looking for.
Using the higher oven temp at the beginning of the bake speeds up the scientific reaction for the production of carbon dioxide (bubbles) which inflate the cake. You're right to keep the oven door shut and reduce the heat because if you open the door, a spell of cold air can knock out the air and cause it to deflate.
Salt is used to balance out the sweetness of your recipe and helps with browning, with bread making it absorbs moisture and helps slow down fermentation. - Also, see
Why do we use salt in baking?
You're welcome on the baking soda/powder by the way.
To make your banana muffins a little healthier you could add some sour cream to the recipe in replacement for some of the banana. It may make them a little lighter and give you a more significant rise.
If your cake batter is thick rather than runny then you may wish to try this:
Fill your cupcake cases to as near to the top as you can and then place them in the oven at the high heat first then reduce down. By doing so, the cupcake starts to create volume instantly rather than travelling up the cupcake case first and then trying to create a dome.
Usually I would say to fill cupcake cases two thirds full, but in this case, they might give you more height by filling them with more batter. That's only if it's a thick mix though, if it's not it will erupt like a volcano and just spillover.
With regards to the job of the eggs, eggs are made up of the whites (water/moisture/proteins) and the yolk being fats. The fats add a richness to the bakes while the whites strengthen the bake. Baking is a science, so once you start swapping and changing the way the structure is made up who knows what will happen. Recipes are created with balance and assist with the scientific reaction so if you wish to add an egg yolk here or a full egg to your original recipe then by all means do. I can't tell you exactly what will happen only what the elements on their own do.
The wholewheat flour in the original recipe is also heavier/denser so will not rise as much as your regular all-purpose flour will do.
Before altering the recipe (seeing as you like it so much) why don't you try some of the above options and see if any of those assist in your quest for the dome and then if you're still not happy then experiment.