Hey David, interesting to see the actual photograph and then the raster of the set in operation.
I definitely agree that you should at least reflow the solder around the HOT and flyback area. I don't know why the greyscale would be off, unless it is due to a software issue(service menu or customer 'temp' control) though since these Trinnys have AKB (auto kinescope balance) which blanks the video out when a drive difference is detected at startup or as the crt ages...blink, blink blink goes the standby LED...
Those are heavy SOBs....we have a kv-35S40 from 1999 still going strong, though I refocused it last year since it sees a ton of use. Haven't reflowed anything since it hasn't moved an inch since taken out of the box.