Like a lot of slingshots in succession, yes. It's the same mechanism as ring shepherding.
Stuff interior to Jupiter overtakes Jupiter in its orbit, and they exchange energy gravitationally: Jupiter slows the stuff down, the stuff speeds Jupiter up.
Stuff outside Jupiter's orbit is overtaken by Jupiter: Jupiter speeds the stuff up, the stuff slows Jupiter down.
The interior stuff, losing energy, moves into a lower orbit; the outer stuff, gaining energy, moves into a higher orbit. Jupiter mediates the exchange and stays pretty much where it is, unless there's a density gradient in the disc.

Grant Hutchison