David B Mehldau's influences range from jazz to classical to pop and even grunge so hard to pin him down with the standard "jazz" musician label. I suppose one would just call it a solo piano arrangement perhaps?
He kept it short and simple there which he does on occasion but when he stretches out he may lose those less inclined to more "outside" playing. The only recordings of Blackbird that I'm aware of on iTunes/Spotify are one trio recording which definitely takes a jazzier turn and one live solo recording that you may or may not like as he stretches out on that one with more improvisation.
I think a lot of his solo playing would be in your "drives me crazy" category but you might enjoy this one as well.
https://www.youtube.com/watch?v=kCfmg-Qut9I
My personal favorite Beatles cover he has recorded is from his Ballads and Blues album but again, this one may veer into territory that you don't enjoy.
https://www.youtube.com/watch?v=EDl9q2gaVwk