The fallen angel song has lower harmonies thickening it up on a lot of it. When he sings high on his own, it sounds similar to the vocals on the new track - and I can see that the 2nd order harmonics are louder than the fundamental on both new and old for these higher reedy vocals.
I reckon the vocal sounds fine in context anyway, leaves space for the bottom end of the guitars
Surfereq isn’t a magic bullet, I tried it on the new vocal you posted, but it was struggling to track the pitch when the singer hit sections where the 2nd order harmonics got louder than the fundamental (it kept thinking the louder 2nd was the fundamental, boosting it even more). You’d have to sidechain it from midi to get it to track 100% accurately.
If you’ve got ozone, I’d use the dynamic eq to tuck in and control the harmonics when they jump out.
As an aside - the mixes sound cool but, personally, I reckon they’d sound even better if you backed off the ozone maximizer by at least 2db. They’re smashing out at -6 LUFS, mowing off all your drum transients. Listen to eg: the latest avenged sevenfold albums, they’re at -11 to -12 lufs and they sound incredible, the drums are so punchy, wouldn’t surprise me if they mastered it that way to mimic the punchiness of the drums on metallica’s black album (since they copied just about everything else ).