Six months ago, I had three offers on the line, and I chose the one I thought was a better fit for me. However, this company was horrible and had some ethical issues going on. As an accountant, I will never participate in unethical situations, so I decided to leave this company. My problem now is that those other companies were on my top list (and still are), but I don't know how to approach the HR managers and ask them to reconsider me as a candidate.
Asking the company to reconsider a previous offer rarely helps, and it only makes you appear foolish and immature. If you are interested in working at a company you have previously rejected, you make a fresh application (perhaps for the same role, or maybe even a new role).
Any reasonable HR or hiring manager knows that candidates rejecting offers is a part of the game. Getting a job offer rejected doesn't mean an insult, it only means that at that time, you decided not to accept the offer due to your reasons.
The situation has changed since then. Reasonable people would recognize that under the new set of circumstances, accepting the offer might work for you. If you are good enough for the role, there's no reason why they would hold a "grudge" for your previous reject and let go of a good candidate.
You must be aware, though, that some companies have a policy about the minimum duration a candidate has to wait before applying for a job again.
Simply reapply. They'll probably ask you in the application whether you have applied before, you should say 'yes'. They will probably find that you were a successful candidate, which hopefully triggers some kind of 'welcome back' reaction from them.
If they ask you at your interview why you left, say why you left in a sentence a two - it was a bad experience but they are not asking you to write a book abut it. In one or two sentences about why you left, leave them with a feeling of confidence about your competence and professionalism which includes your ethics.
In other words, leave the door wide open for them to ask you back in.