Geoserver: How to set custom gridset to default caching using REST

I've successfully added a custom gridset using the Geoserver REST API, but now I don't know how to add it as the default caching grid set. In addition I would also like to adjust the default caching formats for coverage, vector and other.

I've tried finding something in the documentation, without success. I've also tried a PUT request to /gwc/rest/config:

geoserver_request "$GEOSERVER_URL/gwc/rest/config" "$(cat gwcConfig.xml)" PUT

gwcConfig.xml:

<gwcConfiguration><version>1.0</version><defaultCachingGridSetIds><string>EPSG:2056</string></defaultCachingGridSetIds><defaultCoverageCacheFormats><string>image/png</string><string>image/jpeg</string></defaultCoverageCacheFormats><defaultVectorCacheFormats><string>image/png</string><string>image/jpeg</string></defaultVectorCacheFormats><defaultOtherCacheFormats><string>image/png</string><string>image/jpeg</string></defaultOtherCacheFormats></gwcConfiguration>