Yes. The bullet-time player does not really need a trail.

Your version still has problems with synch. There are 2 obvious issues:

1) the bullet time player has several seconds time to experience 1 second of real-time to shoot. If he hits the opponent in second 3 then the real-time player could already be out of the room and is wondering who could hit him there. It would be physically not possible.

2) if the bullet-time player returns then all other players could have left or had several seconds time to shoot you down while you thought it would have been only one second.

It simply would not work this way. Thats why I am suggesting not to change the time. Change the appearance of time instead (e.g. with trails)