Would switching the selection of board members away from shareholders to employees (subject to bribery controls within campaigns, for salaries and stuff) limit the short-termism that the current corporate world seems to face?
In Sweden, 2 employees are members of the board in companies over 25 employees (by law). So at least here, not all board members are choosen by the shareholders.
One of the reasons many shareholders have stocks, is to influence the long term way the company is run. The main way to do this is by influencing which people are on the board. If big shareholders could not influence this, the cost of new capital into the companies would increase very much. Because with less influence there is a larger risk, and the way you pay for larger risk is by larger return on investments.
So in short, while it seems on the surface that it could limit the "short-termism", as you call it, it may actually have the opposite effect.