I will offer my knowledge and experience the same I offer to our Cadets.
but in short - Thin layers of smooth polish.
It doesn’t really matter what polish you use. Kewi, Cherry Blossom, Cadet Direct’s tin, Market stall special, (or even colour) nor does it matter the application pad. Cotton wool, sylvette cloth, duster, tights, Dad’s old underpants. What is critical is a smooth thin layer, built upon smooth thin layers.
Ok so some polishes will offer a “better” finish, either by working quicker, easier to apply or offering a “fuller, deeper” shine or simply last longer. Likewise some applicators will be more successful, it does follow that to get a smooth finish a smooth applicator is required.
Think of it this way, your toe cap is like a pot hole in the road. Do you fill it up with a wheel barrow of dirt and then attempt to smooth it? or do you add a shovel at a time and when near the brim apply smaller amounts to create a smooth, flat finish on the road?
The correct method for smoothest* finish is bits at a time.
Use this approach to your shoes. Once all the polish is stripped away (use a knife blade) Apply thin layers of polish the thinner the better, as each layer builds, ensuring it is smooth, the defects on the shoe’s surface will slowly but gradually disappear.
This approach has served me well for the last 16 years. There really is no need to use heat either candles on the polish or the shoe, no need for a “hot spoon” to smooth the surface. There is no “quick fix” it just requires good old fashioned elbow grease and some time.
*for the best shine a smooth surface is required. Consider the reflection in a mirror or window verse a bathroom mirror. Consider the reflection on a lake at the still dawn verses midday when the wind has picked up creating waves. Which has the clearer reflection?
Now consider a sand beach and a pebble beach. Which of those has the smoother surface? A sand beach….why? because it is made up of smaller grains. Replace the beach with your shoe, and the sand or pebbles with polish. Small “grains” (layers) of polish will create a smoother layer….
For those interested I have used damp cotton wool balls and Parade Gloss for the best part of 16 years and have been happy with the results every time