That looks like an excellent system. Since it has worked well for you, why do you want to change to using the Clipboard History?
As I see it, the Clipboard History Switcher is primarily used for:
You can then paste any previous system clipboard by triggering the Clipboard History Switcher macro. Clipboard History Switcher will present you with a window allowing you to select any of the past clipboard and paste them.
So I use it visually most of the time: (1) Display the Switcher; (2) Double-click on the Clipboard I want to paste.
However, I do use it in an automated way, like in this macro:
MACRO: Paste In Order Copied
I've not really used the Favorites or Search feature, but they might be of interest to you.
You can mark entries as favorites, in which case they will never be removed from the clipboard history. You can toggle a filter to show only the favorites in the search field (top right), or by option clicking on the favorites button.
You can use the search field to filter the clipboards.
Have just now carefully read through the Wiki on Clipboard History Switcher I realize that it probably has functions/features that I could use, but have not do so.
So maybe some experimentation is called for. 