I've had a go at adapting what the club have come up with, rather than creating something from scratch.
For me, the 1878 looks ridiculous on the new badge. Banged in because there's a bit of space for it. I've not seen anyone comment on how unathletic the new shield is, either - it's fat.
The stuff to keep... I'm not a huge fan of the yellow, but the club seem to want it. The tower is actually pretty good - it's a much more accurate representation than the previous tower design. I don't like the 'Everton' text, but I suppose in this globalised world where emerging markets are important, we need to make sure people unfamiliar with us know who our crest belongs to.
So I've replaced the 1878 with the laurel wreaths (they've been either side of the tower on every badge it's been on) and set it all on the outgoing shield shape.
I could live with this.