The 'tab' on the clamping washer should be over the cable.
It should not. If you are doing yours that way I'm surprised that your wheels are even going round
But the OP is going La-la-la to any suggestions, as he's not convinced. Bike shop it is.
OP's responses seem entirely reasonable to me. Pleased he didn't follow your clamping suggestion.
Cables including outers now changed: the 'new' cable looks a bit ropey, I agree. Maybe it's the light.
A good clean and oil of the RD:
still to do. May as well go the whole hog and dismantle the cage, clean the jockey wheels (their tooth profile looks almost as new).
Get the cable in the groove.
Good squirting in the STI:
still to do, but it gives 8 clicks, as designed/required.
I would back the limit screws off and start from scratch.
https://si.shimano.com/en/pdfs/si/5TS0B/SI-5TS0B-000-ENG.pdf