I could be wrong, but I think most companies prohibit their employees from short exposure (shorting equity, being long equity puts, or short equity calls) to the company, even if they're still net long the company.

I may not be understanding your question but I generally have advised my wife to sell most of them as they vest. Having all of your compensation in one company (salary as well as thousands of dollars in stock) is too undiversified in my opinion. They are also much less liquid then you'd think as there are often long blackout periods with short windows to sell so it's quite tough to time the market.

Puts work well if you can acquire the options at a reasonable price (they're often quite expensive though).

Mark Cuban did this when Broadcast.com was acquired by Yahoo!

However, the contracts may be illiquid / not available for smaller market cap companies.

Companies may explicitly bar these.