Yeah -- I've ended up defaulting to jq just because of its ubiquity, but many of these other tools have similar attributes without the esoteric nature of the jq DSL. It'd be great if something more natural came along and actually started to displace it.
I've never felt it was an unnatural API, but it can be hard to grok/remember. I was primarily using jq either to extract data from large JSON files or to concatenate a bunch of smaller JSON files into one, large file.
I think it can get a little weird as far as error handling goes, but I feel it's been pretty approachable.
JSONata remains pretty obscure but it's been my favorite JSON query/mangling DSL for a while now: https://github.com/jsonata-js/jsonata.
jmespath is also quite natural, but I think it was hurt by reference implementation in Python, meaning it's quite slow. http://jmespath.org/