@herf Well, this is odd, and I'm not 100% sure why things changed back to working correctly. I had restarted the laptop several times and the bug remained.
Then I happened to run Cocktail's system cleaning/maintenance routine, restarted my MBP and noted that the f.lux logo started showing correctly again (white logo on black background) in Bartender 2's menu bar as well as the regular MacOS menu bar if I left f.lux there.
I'm still at a loss for this bug, but the pesky issue has gone away. Something corrupted in a cache that was cleared by Cocktail, perhaps?
I'll leave this here as a hint if anyone else runs into this bug after installing MacOS Sierra.