It looks like the flare is starting to show on the whites around two stops beyond maximum black on a fairly contrasty paper/filter. That's not surprising and not something I'd focus much on.
I'm not a fan of trying to set the exposure just by the meter, but a meter reading can get you a decent starting point for a test strip for the highlight exposure and help you get a rough contrast range for a starting contrast grade. Even at it's best it saves just a tiny strip or two of paper and a few minutes of processing.
The difference in contrast between your two prints is possibly based on the cold light head vs the effectively collimated light from the enlarger. I don't know for sure that the Callier effect pertains to contract prints made this way, but it seems like it might. I'd bet that's the primary reason for the background difference and not flare. You could test that with the same lens and a condenser head.
Remember with printing you expose for the highlights, then assess contrast. The multigrade filters are designed to keep the highlight exposure fixed (or with the one stop jump) as you found earlier. So you should be able to make contrast jumps with the same exposure if it was really based on a zone 8 or 9 highlight (in practice I usually end up with another test strip with 1/10th or 1/20th of stop gradations after contrast changes). I think if you tried to match contrast between the two prints there would be very little difference.
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