Check your employment agreement, stock trading policy and options agreement. I would expect the trading policy to apply to employees only, and may not apply to you after you leave employment.
Also, a trading policy probably prohibits buying or selling shares during a closed window, but exercising options for cash (well usually a check) isn't really buying shares. The trading window protects the company from having to investigate (some) insider trading incidents and exercising options with inside information might affect taxes, but wouldn't affect other investors.
Your options agreement should indicate how to exercise them; if the amount you think this is worth isn't enough to justify a lawyer, you should follow the exercise instructions and document thoroughly. Something like mailing a check, addressed to the Tresurer, certified return receipt. Then they've got to do something with the check.
To be clear, have you left yet?