I find it weird if you have to lower the pickup down flush with the plastic ring, I really like my BKPs on the bridge quite close to the strings, but surely also depends on the guitar.
Several components could be "the issue" here. Different guitar cables (between guitar and amp) can make a big difference too. I was all into Vovox, but now find them too bright and clear, and switched to Mogami 2524 for a smoother, but still articulate tone. It's much cheaper too, so I ordered some bulk and some plugs to get things sorted for good on my board.
Wiring obviously, if it's wired vintage (tone cap wired to middle slug on volume pot), change to modern (tone cap wired to input, where the pickup is wired on vol pot) - this also smoothes it a bit even with the pots on full (in my experience).
I can relate to that kind of unpleasant treble you report with the Cornford voicing. Cornford bias their amps quite cold, which is Ok if you can really crank them as the tubes start to work harder at higher blasts and it gets thick and creamy, but at lower volumes (below 10 o'clock) I got better results biasing a bit hotter. At 65% I found the sweet spot with my Mk50 with SED =C= 6L6es, that is 41.5mA per tube on 465V plate voltage.
Could also be other things, new strings after pickup change, etc etc.