By that definition, chess engines would have free will, as they would be able to search a through larger amount of possible moves given the extra time and thus

By that definition, chess engines would have free will, as they would be able to search a through larger amount of possible moves given the extra time and thus find another move. The problem with that definition is that time itself is an external input of sorts. Therefore, everything is not the same since you have +k time. Your definition would also apply to many trivial decision processes, e.g. a computer programme that randomly switches between each possibility and picks the one it ends on when the allotted time has elapsed. I doubt that programme would be considered to have any will at all, let alone free will.