Headphone bleed isn't really all that unusual, and it's usually not a huge deal. The warnings about hearing damage are well intentioned, but we're all adults here, and this is rock n roll (or whatever) and if loud headphones is what it takes to get a decent
performance...
The important question is what's the ratio of bleed to vocal? Like, give us some db readings off the meters, man! The vocal peaks at X and the bleed sits around Y. If the difference is big enough, and unless you're really going to
crush the vocal with insane amounts of compression or distort it, you shouldn't be able to hear the bleed in the context of the mix.
Of course, that assumes that the mix that's bleeding from the headphones is relatively similar to what the final mix will be. Where headphone bleed can be a problem is in situations where you're laying a vocal over a basic click track that will be removed from the final track, or like a drummer listening to a "beep track" which might bleed into some of the drum mics, or things like that where there wont be anything in the final to mask whatever's bleeding through.
Sometimes that bleed is all treble. If you can roll off some of that treble going to the headphones and still stand to sing to it, it will be less in the mic.
Something that might work if every other damn thing is just right and you're very lucky - monoize the headphone mix, and flip polarity on one side. Theoretically if you approach the mic such that each of the two speakers is exactly the same distance from the mic the bleed will cancel completely. It can't possibly be perfect IRL, and it'll probably feel like your brain is being sucked out of your ears, but if you really cant live with the bleed, it might be worth a try.