I have reduced zing on round wounds with a strip of medical tape (cloth type) around the string at the bridge.Just play the strings a lot and dig in a little bit to get them to break in faster.
Anything foreign substance added to the strings now for short-term tone improvement might have unwanted long-term side effects.
If it's still too bright during the recording session, use some foam, pull back on some of your highs & high-mids on your amp's EQ, or explain to the engineer that the new strings are brighter than you want and ask them to tame the top-end a bit if it works on the mix.
So, when I put a new set of flats on one of my basses? I just play the snot out of them until they're actually broken in, and sound like they should. It's good practice; an opportunity to learn new songs; and I don't have to deal with gooky stuff all over the strings...