Why not make the order yourself?
There are many ways to do it. The most simplistic way is, adding delays to each Begin Plays of each BPs.
No Delay = First one to trigger in Game Mode
0.01 Delay = Do something in player BP
0.02 Delay = Do something in player Controller
So it will be guaranteed to happen in order. Surely there are more proffesional ways, but that would be a start I guess. I did that before putting everything into right order so they would work without delays. =)