It does sound similar to ideas in Tahoe-LAFS: https://tahoe-lafs.readthedocs.io/en/latest/architecture.htm...
Which has already thought about attacks on the scheme you described: https://tahoe-lafs.org/hacktahoelafs/drew_perttula.html
Which has already thought about attacks on the scheme you described: https://tahoe-lafs.org/hacktahoelafs/drew_perttula.html