That said, I voted in favor. I don't believe that divestment is a sound strategy for effecting change in companies
I'm confused why you voted for the proposal if you don't think divestment is an effective strategy. The "against" vote recommended by the board is the option that would not allow index fund managers to divest.
The proposal isn't completely about divestment. It reads as follows (emphasis mine):
Shareholders request that the Board institute transparent procedures to avoid holding investments in companies that, in management’s judgment, substantially contribute to genocide or crimes against humanity, the most egregious violations of human rights. Such procedures may include time-limited engagement with problem companies if management believes that their behavior can be changed.
If passed, the proposal would give Vanguard fund managers some latitude about what to do with stock in companies deemed to be engaging in genocide. Divestment is one option, but another option would be for Vanguard to put forth a shareholder proposal for the company to shape up and/or talk to the company's management to urge a change in behavior. If none of those options succeed in a reasonable amount of time, divestment would then be required.
If I were writing the proposal I would put more emphasis on retaining the stock and using those voting rights to create change, maybe even overweighting the company slightly in order to gain more sway over decisions. Like I said, I think that divestment has little effect on a company's behavior, but the other options that this proposal would allow leading up to divestment are something I do believe in.