Thank you for starting this discussion. I think any kind of pedagogical tool should be shared with students and collegues, especially in writing form. When I read "the classics", i.e. works of famous mathematicians I always wondered the process they went through to reach those conclusions, what imagery went through their heads while they proved a theorem, maybe that would be useful to me, or not, but I always wanted to know. I think during a lecture saying something like "here is how I do it, imagine group elements breaking into a formation organized into circular groups" is no discomfort to anyone. Maybe this explanation can help one student, or two (or all) students to grok the topic just a tad more, and that's still important. Richard Feynman used to say (paraphrasing) that he never really knew in advance how his students would understant quantum mechanics, he did not have any single method, he'd only try to explain the topic from many different angles hoping that one of those angles provide an entry point for a student, into the subject.