I like your take on Lennon's voice...everything works...
Funny thing about doing those...
On the original, Lennon's vocal was speeded up quite a bit. Probably about 2-3 half steps. Easy to do back then. VSO the recorder down, record and then speed it back up. Not so easy a stunt in digi-world. There isn't a DAW out there that can do this in one step....with good sounding results. Mostly the shifting algos they use. Particularly when you need to go beyond 3 half steps.
This is what I did. I used a stand-alone shifting program, called "Amazing Slow Downer". The developer created one or two of the best shifting/stretching algos I've ever heard (there are 5 in the program). When it first came out, he hadn't thought to tie them together...they were two independent processes. I wrote him and suggested it....which he did. One of the great features of this program is that whatever you do to the audio can be instantly exported into the audio format of your choice.
So I ran a mix of the instrumental through it and slowed it down by 4 steps ( I tried 3, but I could still hear "me"). That was dumped back into Cubase as a new project where all the vocals were recorded against it. Those, in turn, were rendered out, dumped into ASD and bumped up 4 steps, using the best algo it has for solo instruments/vocals: nice formant shifting and no detectable glitching. The results were saved out as AIFF files and dropped back into the instrumental, in the original key. No edits or alignments necessary. Mixed it and done.
I'll tell you....if I tried to do this at speed, I could have never done it. My 64 year old pipes can't hit those notes anymore....so this little process was quite a saving grace.