Hey, something I've discovered is that animal-vehicle hybrids seem to be a really popular concept in Japan. There's the Catbus from Totoro (as I'm sure you've heard of), along with 炎神戦隊ゴーオンジャー, だいすき! ぶぶ チャチャ, and 南の島の小さな飛行機 バーディー. Maybe you might want to check those out?
English titles, respectively: Engine Sentai Go-onger, Bubu Chacha, Birdy the High Flying Little Plane.
I've heard of all of your recommendations! My personal hypothesis is that animal-vehicles hybrids seems to be fashionable in Japan because of Shintoism.
A polytheistic and animistic religion, Shinto revolves around supernatural entities called the kami (神). The kami are believed to inhabit all things, including forces of nature and prominent landscape locations. (From Wikipedia)
The Catbus is believed to be based on an ancient urban legend where cats, depending on the version, would turn into shapeshifting yokai, or spirit demons. For the three other hybrids, I haven't done any profound research, but it's not far-fetched to think that kami would choose to inhabit cars given the power behind the Japanese automotive industry. And there isn't a proper cult of these vessels per se, but... *gestures hands around* the Western ideal of car ownership and the possessiveness of property and all happened.
I hope you've seen Trailmon from the Digimon world around?