if space-time "grips" photons, such that the cosmologically expanding fabric of space-time stretches photons propagating through said space-time => red-shift ...

 

then would a contracting fabric of space-time compress photons => blue-shift ?

 

 

 

 

Further, what about astronomical red-shifts / blue-shifts, brought about by the time-varying expansion / contraction of the fabric of space-time, near to super-massive / super-dense compact objects ? As they "dance" around each other, in intense interactions, would the fabric of space-time stretch as they sped past, and then contract as they moved on... and would photons flying through said space-time fabric be "astronomically" red-shifted / blue-shifted ?

The answer to your first question is yes. I don't understand what your second question is asking.

if space-time "grips" photons, such that the cosmologically expanding fabric of space-time stretches photons propagating through said space-time => red-shift ...

 

then would a contracting fabric of space-time compress photons => blue-shift ?

 

 

 

 

Further, what about astronomical red-shifts / blue-shifts, brought about by the time-varying expansion / contraction of the fabric of space-time, near to super-massive / super-dense compact objects ? As they "dance" around each other, in intense interactions, would the fabric of space-time stretch as they sped past, and then contract as they moved on... and would photons flying through said space-time fabric be "astronomically" red-shifted / blue-shifted ?

 

For gravitational waves I believe you need changing field - a simple static massive object will not do it; you need rotation or something else similar. And - purely as supposition - I always visualised these waves as transverse waves similar to emr rather than longitudinal similar to a sound wave which is what it sounds as if you are describing. Photons will travel the shortest distance - even that might cause apparent shifts in direction, and I really don't know about red/blue shifts.