Hi Jack,
my try:
I would not put myself in a position where I jeopardized the people working for me, or those for whom I worked, for the sake of vanity.I don't know the exact terms to refer to those words. Let's say those two "past tenses" are kind of like two "subjunctives" or "unreality past tenses". It's like everything is part of an hypothetical statement, like "If I worked there and jeopardized the people...". But that's not really part of an "If... would" sentence, since there are no if's, but rather it is more of a tense simplification in conditional sentences. The simplification consists in using a past tense in conditional senteces, without repeating "would", and it's done even if the situation is real and not hypothetical. Here's an example I just invented:
Well, if some girl tried to flirt with Michael, I would simply tell her he was my boyfriend and to leave him alone. But I wouldn't punch her in the face, come on! I'm not that violent!
First, I'm not sure that's a good example, and second I don't kow if "is" is also possible instead of "was". Maybe it's used in speech the same way mixed conditionals are used, I don't know.
Wait for some other advice