will turn-up with my own lists strapped to my knee and try to take a bit more ownership of the process.
Well, before you go to that effort... Hopefully, by this point, you've been introduced to the flight manual for the aircraft. Every certified plane manufacturer in the last 60 years will have one. It will contain a checklist, which really is the one an only which you should use. The only things which might be added to that would be additional items found in flight manual supplements applicable to the aircraft (ask/have a look, though don't expect much), and items unique to the operation of aircraft at that locale (specific ATC procedures, for example). Otherwise, operate the aircraft with the checklist produced by the manufacturer. Because... If you develop your own, and as a result something is different and missed, somebody will probably ask you why you did not use the manufacturer's checklist, and there's no good answer for that question! If you cannot easily copy the one from the flight manual, write it out for yourself, and make reference on what you've written, that it is a reproduction of the flight manual checklist. It sounds like work, but in doing that, you'll begin to absorb the details and retain them.
As an instructor is being paid to teach you to fly the aircraft, they should be teaching you to refer to a written checklist. If they are not, and are whizzing through a verbal checklist in their head, they are doing you a disservice in your learning. It's not their job to show off how cool they are 'cause they memorized a checklist, it's their job to demonstrate doing things properly. Later in your career, you may choose to memorize checklists, but not now, read the paper every time. And, if you do that, you can completely avoid mnemonics!