I’ve thought about this quite a bit on my own account. The best hedge against owning an option is to, well, sell it. You can’t do that directly through your employer, but you can write call options on the market (with a strike and maturity as close as possible to the ones you own from the company). If the company does well, you owe on your written calls and make money on the company calls. If it does poorly, you pocket the premium on the written calls, which hedges your downside. you’d have to see an accountant because there are potential tax consequences if the government considers it a wash sale.
Also beware of getting fired because you could lose the offset to your position in the market.
Other potential options as mentioned are to short the stock-not recommended, or to buy high strike puts on the stock, which is an expensive strategy.
Would write more, but have to get my daughter to bed.