I default to using their mnemonics because I find it exhausting coming up with that many all on my own, and I do like the way lots of them connect up with each other. I’m going to struggle to come up with my own set of mnemonics that interlink in that way spontaneously.
You say that you rarely care about the stories for vocabulary because most words are jukugo, but they don’t provide mnemonics in those cases anyway…?
The radicals usually look like the thing they’re supposed to be, or are just a kanji you already know; in the former case the ‘mnemonic’ usually just describes the picture for you.
For kanji, I always read the mnemonics, but if something pops into my head instantly I’ll use that instead, and I can usually tell if a particular mnemonic isn’t going to work for me. Often it’s when they use five radicals and I don’t care about most of them or when they can be combined into larger components, but that usually involves tweaking the mnemonic rather than coming up with something entirely new. I see their mnemonics as more of a source of inspiration than the be all and end all
I often find myself using different mnemonics for certain readings. I’m not sure whether it’s a British vs American accent thing, but sometimes the word they pick sounds closer to another reading, and I know I’ll get confused so I use my own. Like ‘cock’ is gonna make me think こく, not かく.