I install 5-10 scopes per month. I follow up with the customers after they live fire zero and shoot a few groups to see how the gun and scope are working. I install scopes on a wide variety of production and custom rifles. I also reinstall scopes on rifles that were exhibiting problems. I frequently see problems that resulted from using cheap rings, improperly installed bases, poorly aligned rings, not lapping rings, and not tightening ring screws to the proper torque values.
For me, the primary objectives of lapping are 1) removing ring misalignment that leads to mechanical stress in the scope tube, 2) making the rings cylindrical to protect the parallax adjustment mechanism inside the forward tube, and 3) maximizing surface contact area to minimize ring marks and prevent scope slip.
To do this, I don't believe that the surface finish needs to be completely removed by lapping. If the grit has only polished the finish, but not removed it down to bare metal, I still consider that area to be lapped. That's because the surface finish is non-compressible.
I usually, but not always end up lapping the rings during a scope installation. I always confer with the customer before pulling out the lapping bar or reamer. Sometimes I conclude the benefits are not worth the effort. If the customer agrees with me, I won't do it. When I do lap, I might stop after the first inspection.
For fully machined tactical rings - like Seekins, Near, Nightforce, etc., on a properly machined and installed rail, I don't usually expect lapping to be valuable. However, if I suspect a poor fit between the rail and receiver, which can cause the rail to bend and/or twist, I will lap the rings, even if they are fully machined tactical rings. I've found that most aluminum rings below a price point of about $75 are not fully machined, but rather have extruded ring surfaces. I always lap rings that have extruded ring surfaces.
In your case I might have stopped lapping at your first photo. The lapping bar contact on your Seekins rings actually might have been uniform enough at that point in the process. It appears as though there were high spots on the leading and trailing edges of the rings when you started. However, I can't tell from the photo how much of the finish in the center area was polished by the grit. If the center area was at least 75% polished I would have stopped there.