Owning a stock via a fund and selling it short simultaneously should have the same net financial effect as not owning the stock. This should work both for your personal finances as well as the impact of (not) owning the shares has on the stock's price.
To use an extreme example, suppose there are 4 million outstanding shares of Evil Oil Company. Suppose a group of concerned index fund investors owns 25% of the stock and sells short the same amount. They've borrowed someone else's 25% of the company and sold it to a third party. It should have the same effect as selling their own shares of the company, which they can't otherwise do. Now when 25% of the company's stock becomes available for purchase at market price, what happens to the stock? It falls, of course.
Regarding how it affects your own finances, suppose the stock price rises and the investors have to return the shares to the lender. They buy 1 million shares at market price, pushing the stock price up, give them back, and then sell another million shares short, subsequently pushing the stock price back down.
If enough people do this to effect the share price of a stock or asset class, the managers at the companies might be forced into behaving in a way that satisfies the investors. In your case, perhaps the company could issue a press release and fire the employee that tried to extort money from your wife's estate in order to win your investment business back. Okay, well maybe that's a stretch.