To start, on the basis that I think it has been agreed that it is possible to be at rest relative to the generalized redshifted light sources and the CMBR,
No, it is not possible and it is not true. You are making multiple mistakes:
1. CMBR is not a frame, so you cannot be "at rest wrt CMBR"
2. The redshifted light sources are galaxies that move at different speeds, so you "could" be at rest wrt to some of such sources but you cannot be at rest wrt to all such sources.
then I hypothesize that we can also be at rest relative to all of the gravitational wave energy sources as well. Do you agree?
Nope, same mistake as above.