My apologies. That was an utter failure on my part.
By way of compensation, some advice and thoughts: I think your requirement of 1-5KHz is the wrong end of the problem you're looking at. Getting from the requirement back to the appropriate solution requires throwing existing approaches away and starting with a specification. Then gain understanding of the problem and research first before applying existing knowledge. From experience comes understanding and from understanding comes simplicity.
Art of electronics chapter 9, available free here:
https://artofelectronics.net/wp-content/uploads/2016/02/AoE3_chapter9.pdf ... see section 9.6 on switching converters.
The trick is to learn the theory first, then look inside all the ICs via datasheets and see how they work. This is neatly packaged up in AoE but you need to go looking further. Then go back to the problem when educated.
You will then see why my assertion that the 1-5KHz and random 1mH inductors is the wrong end of the problem.
I built something very similar a couple of years back. I needed to derive four voltages from a 12V supply, one of which was 2KV. Applying knowledge attained, plus some external research, I built one that worked out of the box first time which had two transistors and a Royer architecture which is as minimal as it gets.
My design, now departed as it was a toy, is similar to the converter shown here:
https://ludens.cl/Electron/scope/scope.png . These can be scaled down to tiny things running with a couple of 2n3904's using a few mA up to 2n3055 beasts delivering 10 amps.
But before all this you need to learn to walk so build some simple R-C oscillators and skip worrying about what they do and the efficiency. In fact if you want to design and build something discrete you need an intimate understanding of the parts. Learning the Art of Electronics, the companion book of the above is great and even covers building boost converters and how they work later on.