Congrats on the career change! Now you are exposed to a different set of risks to your income. You may be a corporate rockstar but that's a relative concept. Most likely, your company's fortunes drift up and down and your contribution is marginal in the big picture. For example, you could bring in $10 million profit one year and yet be a rounding error to many companies. Even larger is the risk to the industry (see fax machines). Seems unfair, but how can you effectively insulate yourself? Think like a hedge fund!
Let's say you have reason to believe that PepsiCo will fare better than Coca-Cola. A naive investor might buy shares in PEP. In reality, this investor is betting on both Coca-Cola AND the beverages industry. KO shares might drop 20% while PEP only drops 5%; congrats on your thesis but sorry about your account. A savvier investor might buy PEP and short sell KO at the same time. Now the exact outlook is reflected in the net trading position. Back to your situation...
As a full-time employee, your position is the opposite of diversification. Your income depends on your firm, while your firm's income depends on your competitive position and the industry's performance/outlook. You may even own company shares in a retirement fund. That's a big bet on one roulette number. Let's apply the hedge fund approach. It may be a bit distasteful to short sell your company's stock, plus you likely believe there is a sunny outlook since you agreed to work there. So, accept the new job offer, then short your industry via an exchange-traded fund. You have now limited your exposure to the relative success of your company to the industry, regardless of the larger economic picture.
Granted, this could be a bit complicated for employees who don't follow finance. A neatly packaged product could help more people cover this risk and greatly minimize the impact of unemployment or economic downturns for the savvy worker. Note that this financial arrangement effectively replicates unemployment insurance cash flows: the employed pay a repeated small amount while working but gets a return when a downturn happens; the method above is similar, but more tailored to the individual and his or her company.