You are right. I'm thinking to handle this by giving the initiative to all party members. Shadowdark is so oldschool it doesn't think about virtual tabletops, so giving the initiative bonus to all party members means the party will benefit no matter who's sitting where. I think.)What I was referring to is that the only initiative roll that matters is the highest one, since the order then just goes clockwise around the table. So it has (mostly) the same result as just giving the bonus to one player of your choice.
(Mostly, but not exactly. There are very gamist circumstances in which giving the bonus, if it's large enough, to a player of your choice is better than giving it to everybody.)