Is it possible to assign different shortcuts to different tasks in VS Code?

As of VS Code 1.10, you can use the workbench.action.tasks.runTask command in your keybindings, and pass in the task’s name as your argument.

The VS Code task documentation gives this example:

{
    "key": "ctrl+h",
    "command": "workbench.action.tasks.runTask",
    "args": "build"
}