How can I control the log level for the JSON API?

It does not provide a command line parameter to do so. Is there an alternative way to set it?

I’m not sure there’s a clean way to set it when you start using daml json-api. If you use the standalone JAR, you should be able to pass in logback config using java -Dlogback.configurationFile=... -jar ....
The default JSON API logback config is in ~/.daml/sdk/1.4.0/daml-sdk/json-api-logback.xml. I don’t recommend manipulating it, but I think it can reasonably serve as a template.

The logback file is your only option atm.