Logging formats for errors

We configure HAProxy log format for each frontend to output JSON which is then parsed by our centralised logging system.

This works fine for normal traffic, but we seem to get a lot of SSL handshake failures from clients, and when this occurs, HAProxy ignores this JSON format, and outputs plaintext, so we get a lot of JSON parse errors like:
JSON object is not an object; input='172.18.0.1:42770 [03/Aug/2018:11:46:05.649] port_443/1: SSL handshake failure'

Is there a way to configure the “error” log format HAProxy uses?

Our config looks like:

global
  log 127.0.0.1 local0
  log 127.0.0.1 local1 notice
defaults
  log global
  mode http
  log-format "{\"timestamp\":\"%tr\",\"method\":\"%HM\",\"host\":\"%[capture.req.hdr(0)]\",\"path\":\"%HP\",\"query\":\"%HQ\",\"uob_username\":\"%[capture.res.hdr(0)]\",\"useragent\":\"%[capture.req.hdr(1)]\",\"client\":\"%ci\",\"referer\":\"%[capture.req.hdr(2)]\",\"duration\":\"%Tt\",\"size\":\"%B\",\"status\":\"%ST\",\"sslcipher\":\"%sslc\",\"sslversion\":\"%sslv\",\"sls_tag_0\":\"neptune\",\"service\":\"%b\",\"sls_tag_2\":\"%s\",\"sls_service_level\":\"${SERVICE_LEVEL}\",\"x_forwarded_for\":\"%[capture.req.hdr(3)]\"}"
frontend port_443
  log local-traffic-logger len 65535 local0