If you go back to your original idea of a 34063, it's datasheet shows how to use an external NPN or NFET as the main power switch in a boost converter.
A 4A boost is not a hard circuit although you will need a good inductor capable of 10A or so without saturating.
A 4A boost is not a hard circuit although you will need a good inductor capable of 10A or so without saturating.