Akinbo,
"more to cosmological modeling not dynamics" is illogical gobbledegook. Cosmological modelling IS dynamics! Our only 'eyes' are spectroscopic. All of cosmology is about motion, from the so called 'Big Bang' and inflation to accelerating expansion, and all 'peculiar velocities' between.
The 370km/s is not anomalous at all just poorly understood, particularly outside astronomy. We are all 'flat Earthers'. We insist we understand what 'motion' is so refuse to consider it any more carefully. That's the 'new way of thinking' needed. Give this a try;
All stars are 'systems', moving wrt other stars complete with all the planets and junk inside their 'heliospheres', the dense plasma 'sheath' defining the limit of the solar winds (radiating at a speed WRT the STAR!) and so the edge of the system. We can often see these in the optical by means of the nebula gas they move through.
The 370km/s is Earth's speed wrt our OWN star, NOT any others! It is also NOT wrt the galaxy as the solar system has a ANOTHER orbital velocity wrt the galactic cente. But again, the galaxy is also system, with it's halo, which is NOT absolute, i.e. others are different, and they all move wrt their "local group" rest frame. etc etc etc. It is a heirachy. A hierarchy of inertial systems wher;
ONLY THE 'NEXT FRAME UP' IS A VALID DATUM FOR MEASURING PROPAGATION VELOCITY
Does that help at all to give you a glimpse of the big picture, supposedly 'anomalous' but rationalised by 'discrete field' dynamics?
Best wishes
Peter.