I agree about singing in a different key so you don't have to shift a full octave. You can copy one track (like piano) transpose it up a few steps, mute everything else, and sing your part with the piano (or guitar or whatever) as your guide. Then you can shift your voice up less than an octave and tweak the formant.
I doubt you will be 100% happy with this, but it all depends on the individual's voice. It may work great for you.
It is amazing how many female singers will be happy to help with some studio work for little or no money, just because they enjoy it or want the experience (or because you're friends). I'm sure you've thought of this, but keep in mind that the female singer does not have to be perfect because you can fix her part with Melodyne. Better to tweak her pitch a bit than shift yours a whole octave. And you can always lower her formant just barely to make her voice blend better with yours. This isn't what you're asking: it's just an idea.